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Succeed in Bonds Even if You Don't Know Where to Start

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Buy America’s best corporate bonds at possible high-yield returns, clear savings recovery time & less risk than stock!

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- 1 hour on-demand video
- 2 Articles
- 1 Supplemental Resource
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

- Manage a portfolio of bonds regardless of the mix of quality, coupon, or maturity.
- Immunize a large bond portfolio from risk of interest rate increases.
- Rebalance when bonds mature or are called.

Requirements

- Basic arithmetic.
- Competency in a spreadsheet program such as Microsoft Excel.

Description

(Scott--

Thanks for link, but it really doesn't allow me to (1) delete my earlier comments or (2) submit my retraction. If you can do either or both of these things, please do so with the comments below. Thanks. George.)

Dr. Brown:

I want to revoke and delete the recent criticism I wrote concerning your Bond Investment course. It was excessively negative and unfair.

I think my comments were prompted by my ignorance of Bond Investing. I knew nothing about bonds, and because of this, I expected your course to make me an expert in an hour or two. Not very realistic….

I now realize that the course delivered all it promised to do; I realize also that the real learning will begin, only when I take your principles and begin to research and apply them further. The course offers very clear direction....

No one has contacted me or pressured me to write this. I was simply wrong....

Again, my apologies.

Best regards,

George Kirazian

San Diego, CA

---

Bond investorsThese plans pump **dumb money** into the
market by the billions.

Big drops in** interest rates** coughed up
double digit returns to astute fixed income investors like Bill Gross. I know you are not **Bill Gross**.

You don’t have his **training **— yet. But someday you will **deal **with bonds — one
way or another.

Don’t you **agree **that the bond market is a
very real threat to your family wealth if you don’t understand it?

Or perhaps you already have had contact
with **bonds**. Do you have a wealthy
relative asking for guidance in managing their large bond **portfolio**?

This innovative course takes you by the
hand and walks you through the process of managing a **multi-million-dollar bond
portfolio**.

I am Dr. Scott Brown. I am a professor of
finance of the **AACSB Accredited** Graduate School of Business of the University
of Puerto Rico. I train hundreds of
financial managers every semester.

I hold a Ph.D. in finance from the
**University of South Carolina** and a master degree from Thunderbird Graduate
School of International Management.
**Thunderbird **is routinely ranked #1 in the **U.S. News & World Report**.

Here are just a couple of the tremendous **benefits **you will
gain from this training.

- Develop a
**mastery**of bond mechanics through knowledge that will lead to insight over ensuing years. - Understand why
**short**duration bond portfolios allow you to wait it out. - Avoid bond mutual funds that lock you into
**losses**from infinite duration.

Utilize the core knowledge to understand
when to **speculate**, when to go for **monthly income** and when to sit it out in
cash.

Here is what my students **say **about my
courses,

“THERE SIMPLY ISN'T ANYTHING COMPARABLE TO THIS COURSE!” -BILL BAKER, CHARLESTON, SOUTH CAROLINA

**Enroll Now.**

It takes time for your **brain **to absorb and dominate this
material. The sooner you **start**, the
better off you will be as steward of your family wealth.

The material is **guaranteed **in its accuracy
and detail.

What’s **holding **you back? Enroll **now**.

**WARNING**: I am serious when I tell you that
it takes years to **master **a subject. The
longer you delay the slower your **growth**.

Don’t forget that this is the **only **bond
management course available today by a major state university professor for public
consumption. **Enroll **now. I look forward to **mentoring **you in bond
portfolio management. **-Doc Brown**

Who is the target audience?

- Heads of households who save who invest.
- Students of finance who may manage bonds.
- Finance professionals looking for a concise yet complete review.

Students Who Viewed This Course Also Viewed

Curriculum For This Course

8 Lectures

46:50
+
–

Improving Your Life with Bond Basics
5 Lectures
30:14

Hi, I am your guide to **bond **investing. I am Dr. **Scott **Brown.

I hold a Ph.D. in **finance** from the University of South Carolina. I also hold a master degree in international management from **Thunderbird**, ranked #1 routinely in U.S. and News World Report.

I am teaching this course because I have noticed that very few **retail **stock investors understand how to buy and sell bonds.

This is troubling considering that most taxpayers who contribute to employer sponsored 401(k) plans blindly pump trillions into the bond market through poorly understood menus of **fund **selections. **Timing **is everything when it comes to succeeding in bonds.

In the early 2000s interest rates **plummeted**. A risk-free bond portfolio would **yield **you 6% without a thought.

Much higher returns were available in **corporate **bond portfolios if you wanted to think (a little) to grow rich.

You would have been tipped off by an **inverted **yield curve. And long **durations **made the most sense.

But when rates hit bottom rises through come through hike after hike from the federal **reserve**. During times as interest rates rise short durations make sense; but only if the stock market is **dropping**. Otherwise moving out of bonds into equities is more **prudent **in a bullish stock market.

Just get out when you are **unsure **it is the right moment to be in bonds. Or better yet don’t get in when the bond market goes **against **you.

Regardless, this course is designed to give you the **tools **to make such analysis and to take appropriate action through independent thought.

This an intensive program on bond portfolio **management**. This course is helpful for **saving **heads of household who invest; as well as finance students and professionals.

At the end of this course, students will be able to manage a portfolio of bonds regardless of the mix of **quality**, coupon, or maturity. You will also know how to **immunize **a large bond portfolio from risk of interest rate increases. And, you will know how to re-balance when bonds mature or are **called **in.

I will also give you clues to show you how to speculate **intelligently **in bonds. In this course, you will **learn**,

**Section 1:**Welcome to this $82.2 Trillion Global Debt Market!*Introduction:*Dr. Brown Welcomes you to This Wealth Management Course.

**Section 2:**Improving Your Life with Bond Basics*Lecture 1:*How Bond Yield & Price Can Make You Rich

*Lecture 2:*Are Interest Rates as Bad as you Think?

*Lecture 3:*Bond Rating Agencies Are the Bullies of Wall Street

**Section 3:**How Bond Portfolio Management Could Help*Lecture 1:*Are Bond Risks Part of a Right-Wing Conspiracy?

*Lecture 2*: How Duration Could Make you a Better Bond Investor

Learning is **reinforced **by banks of questions designed to test what you retain. Please ask **questions **on the forum when it will help other students. Otherwise direct any questions you don’t feel like sharing with other students by sending me a direct **message**.

The **possibilities **are endless in bonds. Maybe you will be the next **Bill Gross**.

**Gross **is the "*king of bonds*." He is the world's best known **bond fund manager**. Mr. Gross founded the **PIMCO **family of bond funds. He was the first portfolio manager inducted into the **F****ixed-Income Analyst Society Inc. (FIASI) **Hall of Fame. This happened in 1996 for his contributions to bond management.

Bill Gross is known for his ability to **change **directions without hesitation in response to shifts in the markets.

**SmartMoney **in 2005 recorded that "*Gross doesn't adjust to market conditions – he changes them! His views on the bond market are widely followed by professional investors and the investing public worldwide*." Bill left PIMCO for **Janus **Capital Group in September 2014.

He is a **Duke **University graduate who finished in psychology in 1966. Gross spent a summer playing professional **blackjack **in Las Vegas. He served as a naval officer on a **destroyer **off the coast of Vietnam. After the Navy, Gross obtained his MBA in 1971 from the **University of California, Los Angeles**.

He became a **Certified Financial Analyst (CFA) **while working as an investment analyst with Pacific Mutual Life in LA from 71’ to 76’. He was an **Assistant Vice President **managing fixed income securities.

Then he founded and became the managing director and chief investment officer, for **Pacific Investment Management Company (PIMCO)**. This became the world's largest fixed-income management firm.

**MarketThoughts** reports that Bill Gross "*believes that successful investment in the long-run (whether in bonds or equities) rests on two foundations: the ability to formulate and articulate a secular [long-term] outlook and having the correct structural composition within one's portfolio over time*." A three- to five-year **forecast **forces an investor to think long term avoiding the destructive "*emotional whipsaws of fear and greed*."

Bill Gross **says **that "such emotions can convince any investor or management firm to do exactly the wrong thing during irrational periods in the market." Gross **posits **that "*those who fail to recognize the structural elements of the investment equation [asset allocation, diversification, risk-return measurements and investing costs] will leave far more chips on the table for other more astute investors to scoop up than they could ever imagine*."

In 2016 the **net worth** of Bill Gross is estimated at 2.4 billion USD.

This course will prepare you to understand the structural **elements **of the investment **equation**. Let’s **begin**.

Preview
06:16

STOP: Download, Print and Read Course Notes Now!

00:07

A bond is a **debt security **that forces the government or Fortune 500 issuer to make payments to the investor over the time to maturity. Face Value has the same meaning as **Par Value**.

The face value is the payment to the bondholder at bond **maturity**.

The **Coupon Rate **is the annual **interest **payment to the **bondholder**. This is per **dollar **of face (par) value.

A **Zero-Coupon Bond **pays no coupons, sells at a discount, and makes just one payment at maturity to the amount of face (par) value.

Here is an **example**.

You save $1,000 and buy a **30-year bond**. The bond has a **par value** of $1,000 and a coupon rate of 8%.

The **issuer **will pay eight percent of the par value in 60 payments twice every year for three decades. That’s $80 per year in two $40 payments **bi-annually**.

This doesn’t sound like **much**. But a family owning $1,000,000 of these bonds would earn **$80,000** per year in interest in this scenario.

This represents a solid middle class **income**. The median household income for the United States was **$55,775** in 2015 per the **Census **ACS survey.**Retail Prices and Yields in U.S. Treasury Bonds**

Treasury **notes **have maturities that range from 1 to 9 years. Treasury **bonds **have maturities from 9 to 30 years.

The table below shows the prices for a $1,000 par value **Treasury **bond with a 6.25% coupon that matures in August of 2023.

The **bid **prices are what buyers of the bond are willing to pay today. The **ask **price is the level at which sellers hope to unload their bonds.

The bid and ask are **quoted **as a percentage of par value. The **ask **price is 137.438.

This **translates **into a cost of $1,374.38 should you desire to purchase this bond.

The last column is the **yield **based on the ask price. This average rate of return of 2.598% is the ask yield for an **investor **who buys on that day at the ask price of 137.438 and holds to maturity.

**Bond Pricing with Accrued Interest**

The quoted prices in the last table don’t include **accrued **interest. This **builds up **in the six months between payments.

**Accrued Interest**=Coupon/2 X (Days Since Last Coupon)/(Days Between Coupons)

This formula generates the **precise bond value** on any given day of the year.

Corporate **listings **give details that allow you to identify the bond by issuer name or symbol. The **stated **coupon and initial maturity guide investors as to the total return and length of time that the debt will be working. **Statistics **throughout the day include the high, low, and last (close) price with the range of change. Finally, the **yield to maturity** allows investors to know what the yield on the bond is if purchased on the date of the listing.

Notice that the **yield **on the bond is higher the lower the rating.

**Characteristics of Bonds**

Corporate bonds frequently have call provisions embedded in the **indenture**. This is a contract between the firm and bond holders. A **callable **bond allows an issuer to repurchase debt. This may be at a fixed or indexed price. This is done over a specific time known as the **call period**.

**Analysts **refer to this as “*calling in debt*.”

**Convertible bonds **can be exchanged for shares of common stock. This offers an interesting back door entry to **invest **in stocks. Value investor **Mohnish Pabrai** writes of his success in convertible bonds in his book “*The Dahndo Investor*” available on **Amazon**.

**More Quirks of Bonds**

Another corporate bond is **puttable**. In this case the bond holder can **exchange **for par value.

He or she can also **extend **the maturity for years. **Floating **rate bonds automatically reset pricing on set dates.

This is **contractual **and is out of the control of managers.

This is different than the **make-whole callable bond** that resets the pricing based on prevailing interest rates should the firm call the bond. The decision to call a make-whole bond is within the **discretion **of firm managers.

**Even Stranger Bond Realities**

Preferred stock pays a dividend like some **common stocks**. But it is fixed like a **coupon **payment.

**Individual retail investors** cannot deduct the dividend payments from taxes. **Fortune 500 firms** pay less tax on preferred dividends received.

For this reason, the clear majority of investors in preferred stocks are other Fortune 500 firms.

**Other Bond Players**

Public schools, roads and bridges are **financed **by states and municipalities by bonds. These are **municipal **bonds.

**Farm Credit **agencies also issue bonds. So does the **Federal Home Loan Bank Board** that presides over Ginnie Mae, Fannie Mae, and Freddie Mac.

**International Bonds**

Foreign bonds are issued by borrowers selling debt in a different **country **in its currency.**Eurobonds **are denominated in issuing country currency rather than that of the country in which the debt is sold.

**Modern Bond Market Innovations**

It pays to read the bond **covenants**. The **coupon **rate on inverse floaters falls when interest rates rise. Another odd bond is the asset-backed bond. **Cash flow** from assets specified in the bond indenture service the debt

Issuers can pay interest in cash or via **pay-in-kind** bonds.

**Catastrophe **bonds offer higher coupon rates to investors for taking on risks. These perils range from **earthquakes **to hurricanes.

Indexed bonds fluctuate based on a **commodity**. Treasury Inflation Protected Securities are **TIPS**. The par value of the **TIP **rises with the **Consumer Price Index (CPI)**. The** nominal return** is calculated as follows.

**Nominal**Return= (Interest+Inflation)/(Initial Price)

The real return is calculated with this **formula**.

**Real**return= (1+Nominal return)/(1+Inflation)-1

**TIPS Principal and Interest Payments **

This table shows the **payment **calculations for a TIP issued at 4%.

The **inflation **runs at 2% in the first, 3% in the second, and 1% in the third as each of three years unfolds. The par value is **adjusted **by recalculation of a 4% coupon each year. This **yields **a new coupon payment at the end of the first year of $40.80, then $42.02 at the end of the second, and a final payment of $1,103.55.

This is higher than what the **bondholder **would have received at a flat 4% rate on straight $1,000 par value. The additional amount compensates for **inflation **over time.

The bond value is the present value of **coupons **plus the present par value.

**Value **= PV-Coupon + PV-Par. The mathematical expression is,

Bond value= ∑_(t=1)^T▒〖Coupon/(1+r)^t +(Par value)/(1+r)^t 〗

The **maturity date** is T. The discount rate is r. The bond price is **obtained **through a different formula.

Bond **price**=(Coupon) 1/r [1-1/(1+r)^T ]+(Par value) 1/(1+r)^T

This can be expressed in a time value of money **table **format,

Bond price = Annuity **factor **(r,T) + Par value x PV factor (r,T).

These formulas may look **daunting **but remember that they are hard coded into computer systems that report bond values and prices today. Hence, you will **never **calculate these.

But these formulas allow you to see the **intuition **of the inverse relationship between interest rates and bond values. Notice that the interest rate is in the **denominator**.

Hence, bond values and prices **fall **as interest rates **rise**. This explains the **inverse **relationship between interest rates with bond values and prices.

**Bond Logic**

Bond pricing and **valuation **formulas show us that prices fall as interest rates rise. This emphasizes that the main source of **risk **to a bond portfolio is from increasing interest rates. Longer maturity bond values are even more price **sensitive **to interest rate fluctuations.

**Graph of the Inverse Relationship between Bond Prices and Yields**

This figure shows the **inverse **relationship between interest rates and bond prices with a coupon of 8%. Bond prices rise as **interest **rates fall.

Preview
07:58

**Bond Prices Over Different Interest Rates**

This table uses the example in the prior graph of a **30-year bond** with an 8% coupon to extend the study of the inverse relation between interest rates and bond prices. Notice that the higher the **sensitivity** of the price at different market interest rates the longer the maturity. The bond trades at a **premium** below 8% market or is **discounted** above.

**More Bond Pricing**

Bond **pricing** between coupon dates is calculated as, Invoice price = Flat price + Accrued interest

Bond pricing in **excel** is easy with this function,

=**PRICE** (settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of par value, number of coupon payments per year)

**Valuing Bonds **

Do you know how to use a **spreadsheet**? Here is how to set one up for **valuing** bonds.

Here is how Excel can be used to **calculate** values for the 6.25% coupon January 2012 bond from the last figure.

Make sure that you input the coupon rate and yield to maturity in **decimals**. You have to use both the maturity and **settlement** dates in the format DATE(year,month,day). The **value** of the bond (invoice price) is 137.444.

This is cel B12 in the **spreadsheet**.

This example also shows how to **calculate** between coupon payments using a November 2039 4.375% bond. The flat price is 111.819.

Remember that **flat** price is the cost of a bond without accrued interest. The **full** price is the price paid by the retail bond investor.

You also see the **formula** used to calculate the days in the coupon period and the days since last coupon to set up the valuation between coupon payments.

This allows you to find the exact value of the **accrued** interest at 1.094%. You also see how to **calculate** the value of a 30-year bond with a 5% coupon rate. This **price** is 81.07% of face value.

**Understanding Bond Yields**

**Yield to Maturity **is the discount rate that equalizes the present value of a bond’s payments to its market price. This is the same estimation as **Internal Rate of Return (IRR)**.

The **Current Yield** is different than the yield to maturity. It is the annual coupon payment divided by bond price.**Premium** Bonds are priced above par value. **Discount** Bonds sell below par value

**Calculating Yield to Maturity**

This spreadsheet shows how to calculate yield to **maturity** with the Excel formula.

Semiannual coupons Annual coupons

**Settlement date**1/1/2000 1/2/2000**Maturity date**1/1/2030 1/2/2030**Annual coupon rate**1/0/1900 1/0/1900**Bond price (flat)**127.676 127.676**Redemption value**(% of face value) 100 100**Coupon payments**per year 2 1

Yield to maturity (**decimal**) 0.06* 0.0599

*The Excel formula entered here is =YIELD(B3,B4,B5,B6,B7,B8) = 0.06

**More about Bond Yields**

**Yield to Call **is calculated as is YTM. Here, time to call is replaced by **maturity**. Then **par** value is replaced by call price. Premium bonds tend to be **called** more often than discount bonds. This is because the firm can **reissue** debt at lower rates rather than continuing to pay the higher than market interest rate of premium bonds. On behalf of **shareholders**, the firm managers are getting a better deal than market rate when issuing discount bonds. Hence they call premium bonds more **frequently** and discount bonds **less**.

**Bond Pricing for Callable and Straight Debt**

Bond pricing is a function of the **prevailing** market interest rate. This is illustrated with the **blue** line. This is a $1,000 par value bond at 8% coupon with 30 years to **maturity**.

The **black** line is the pricing relationship of a bond that is callable at 110% of par value at a price of $1,100. Notice that such a bond will not have an accurate yield to maturity if the bond is called before it **matures**.

For this reason, analysts are more interested in yield to call on **callable** bonds. This is especially so when interest rates are **dropping** and the probability of calling the bond is rising. This is most **true** for premium bonds selling near the call price.

Most **callable** bonds have several months of call protection where the callable bond cannot be called. Also, **deep-discount **bonds that sell far below the call price are not likely to be called.

**Yield to Maturity and Realized Compound Returns **

The realized **compound** return is the rate of return on bonds with all coupons reinvested to maturity

Horizon **analysis** is the analysis of bond returns over the years. These are based on **forecasts** of the bond’s yield to maturity and investment options. This is done to **reduce** the investment risk.

**Reinvestment** rate risk represents the future value uncertainty of reinvested coupon payments.

**Growth of Capital**

Panels A and B show a horizon analysis for two **reinvestment** rates. At an interest rate **lower** than 10% the final value of the investment will be less than $1,210. But what if the **actual** rate earned is 8%? In this case the **investment** will grow to just $1,208.

Now **suppose** you purchase a 7.5% annual coupon bond for $980 that matures in 30 years. You will **hold** it for 20 years when you estimate the yield to maturity will be 8% and coupons will be reinvested at 6%.

The bond will have 10 years **remaining** and a forecast sales price based on an 8% yield to maturity of $966.45. The futures **value** of the 20 coupon payments is $2,758.92. Adding these two figures **implies** that your $980 investment will grow into $3,725.37 in 20 years.

$980(1+r)^20=$3,725.37 where r = 0.0690 = 6.90%

**Bond Pricing Throughout Time**

Yield to maturity measures the **average rate of return** (RoR) if the investment is held until the bond matures. The **Holding Period Return** is the Rate of Return over the investment period; it depends on the market price of the bond at end of the period.

**Price Paths of Coupon Bonds with Constant Market Interest Rates**

Notice that the **price** of a premium or discount bond will equal par on the maturity date. The price of a **premium** bond will drop.

The **discount** bond will increase in price until maturity.

**How Bond Prices Change Over Time**

Zero-Coupon bonds and Treasury **STRIPS** help us understand bond pricing mechanics.

A Zero-coupon bond pays no **coupons**. All return comes from price **appreciation**.

These are created through **Separate Trading of Registered Interest and Principal of Securities (STRIPS)**. Treasury debt is used to create zero-coupon bonds from **coupon-bearing notes** and bonds.

**30-Year Zero-Coupon Bond Pricing over Time at Constant 10% Yield to Maturity**

A **zero-coupon bond i**s an original issue discount bond where all return comes from depreciation. There are no coupons. Pricing is depicted in this **graph**. Notice how dramatically the price of the zero **increases** approaching maturity.

**After-Tax Returns **

Bond investors must pay taxes on Zero-coupon** implied interest**. Original-issue discount bond time to maturity price increases are implicit **interest** payments to the holder. The IRS views these as built-in price **appreciations** and thus taxable.

A price appreciation schedule is **published** by the IRS that references taxable interest income on the zero-coupon bond at https://www.sec.gov/answers/zero.htm. Zero coupon bond **appreciation** federal, state, and municipal revenues are examples of a phantom tax.

Phantom taxes can also occur in **real estate transactions** and when buying or selling a business. Financially **unsophisticated** investors suffer from financial shortfalls from unplanned phantom taxes.

**Phantom** taxes are common on real estate short sales. The home **owner** is short the money to cover the cost of the mortgage.

The lender has the right to file a **tax return** on behalf of the borrower for the unpaid debt. The IRS treats this as **income** because the borrower did not have to pay the debt.

Taxes are **assessed** on income that the borrower did not actually earn. This is a tax on **phantom** income.

It is your job as an investor or business manager to carefully investigate the tax **ramification** of every transaction you structure. The **onus** is on you.

**Bond Pricing and Default Risk**

An investment grade bond is rated **BBB** and above by S&P. Alternatively **investment** grade is defined as Baa and above by Moody’s. A **speculative** grade bond (a.k.a. junk) is rated BB or lower by S&P. It is also defined as Ba or lower by Moody’s. This low level of bond quality is also alternatively termed **unrated**.

Are Interest Rates as Bad as you Think?

08:24

**Bond Ratings**

Here’s how **ranks** are displayed.

**Default Risk Affects Bond Pricing**

Each differs **slightly**. Investment grade bonds are rated **BBB** and above by S&P. These same bonds are **Baa** and above by Moody’s. Speculative grade or junk bonds are rated BB or lower by S&P, Ba or lower by **Moody’s**, or unrated.

These same **agencies** still command the market despite fraudulent CDO ratings as described in the movie, “*The Big Short*.”

**Bond Safety Signals**

There are a group of financial ratios that are derived from the income statement and balance sheet known to **impact** bond ratings. These **shift** as ratios change each quarter when a public company that issues bonds reports financials.

As bond **safety** ratios fluctuate so do ratings from these agencies. As the **ratings** change the actual bond prices fluctuate through the market process at bid and ask.

This is how changes in financial statements impact bond prices in seconds following release of **quarterly** financial data.

The coverage ratio shows you how company earnings relate to **fixed** costs. Leverage ratios relate **debt** to equity.**Liquidity** ratios are also important. The current ratio links current assets to current **liabilities**.

The **quick** ratio shows assets excluding inventories with respect to liabilities. The **profitability** ratio measures the rate of return (RoR) on assets or equity. The **Cash flow-to-debt **ratio shows you the total cash flow to outstanding debt.

**Financial Ratios Are Linked to Default Risk**

I cover each of these **ratios** extensively in the value investing course. Notice that strong ratios are associated with strong **ratings** and vice versa. A **Value-Line** subscription allows you to filter across thousands of firms with these parameters of these key financial ratios.

**Bond Indentures**

The **indenture** is a contract between bond issuer and holder. The sinking fund is an indenture clause calling for the **issuer** to periodically repurchase bonds before maturity.

**Subordination Clauses**

Subordinations are **restrictions** on additional borrowing. **Senior** bondholders are paid first in bankruptcy.**Collateral** is a specific asset pledged in case of bankruptcy (default). At the opposite end of the fixed income spectrum is a **debenture**. This is a bond with **no** collateral.

**Default Risk and Yield to Maturity **

The stated yield is the **maximum** potential yield to maturity of bond. The default **premium** is the increase in promised yield that compensates the investor for default risk. Bond ratings **plummet** as the risk of default increases.

The risk of **default** increases with erosion of these key financial ratios.

As bond ratings **plummet** the default premium rises. Hence, there is an **inverse** relationship between bond ratings and default premiums.

**Corporate versus 10-Year Treasury Bond Yield Spreads**

Notice the fast **surge** in credit spreads from 2008 to 2009. This was when Lehman Brothers went bust in August of 2008.

**Credit Default Swaps (CDS)**

A Credit Default Swap is a **CDS**. It was **designed** as an insurance policy on the default risk of a corporate bond or loan. It allowed lenders to buy **protection** against losses on large loans. It was later used to **speculate** on the financial health of companies. The resulting financial **debacle** is chronicled in the movie, “*The Big Short*.”

**Credit Default Swaps (CDS) Prices**

As credit conditions **worsened** the price of credit default swaps (bond insurance) increased. Notice how prices of 5-year credit default swaps on U.S. banks maxed out in August of 2008 when **Lehman** collapsed.

**German Sovereign Debt**

Credit default swaps are also used to insure the **sovereign** debt of countries. Notice how the 2009 **recession** in the aftermath of the big short drives up prices of German credit default swaps. Then the **German** CDS was pummeled again by the Greek debt crisis as prices maxed out.

**The Yield Curve**

Yield Curve is a **g****raph** of yield to maturity as a function of term to maturity. The Term **Structure** of Interest Rates is the relationship across yields to maturity and terms to maturity across bonds. The **Expectations** Hypothesis states that yields to maturity are determined solely by expectations of future short-term interest rates.

**Returns from Two 2-Year Investment Strategies**

What if **everybody** in an 8% interest rate market believes that interest rates will rise to 10% next year?

Investors earn 8% in the first year and 10% in the **second**. They buy the one year **bond** and roll into the second year.

You would expect about 9% as an **average** return.

The **investment** will grow by a factor of 1.08 and 1.10 in the first and second year. This is an **annual** growth rate of 8.995%.

It **represents** a growth factor of 1.089952 = 1.188. **Notice** that 8.995% is slightly less than 9%.

Two-year bond investments must return 8.995% to be **competitive** with the current one year 8% bond.

This is an example of **expectations** hypothesis that asserts that the slope of the yield curve changes with short term rates. In this paradigm, the expected holding period returns on **bonds** should be equal.

Notice how the graphic shows that these two **strategies** are exactly equivalent. Investing in two **consecutive** one year bonds, one at 8% and the second at 10% yields the same 1.188 cumulative expected return as investing in a two-year bond.

**The Forward Rate**

Don’t confuse the bond forward rate with that of **Forex**. This is the **Return on Investment (ROI)** that equalizes the expected total long term bond return with that from rolling short-term bonds. This **formula** is useful for estimating the liquidity risk premium.

The **liquidity** preference theory states that investors require a risk premium on long-term bonds. This liquidity **risk** premium is a little extra expected return investors require for taking more risk while waiting for the maturity of long-term bonds. This is measured as the **spread** between the forward Return on Investment and the expected short sale.

**Yield Curve Examples**

Two possible yield curves are **plotted**. In panel A the market expects interest rates to **rise** over time. In panel B rates are expected to **fall**. But the curve is not **inverted**. The liquidity premium gives it a **hump**. Hump shaped curves are not nearly as predictive as **inverted** yield curves. In the case of an inverted curve public **opinion** of futures interest rates are so strongly negative that any effect of a liquidity premium is washed out.

Interest rates are thus **linked** over the years forward.

This theory **predicts** that an inverted yield curve is highly predictive of an impending decline in interest rates. This has been supported by extensive **empirical** work in academic economics and finance.

An inverted yield curve is a door to **El Dorado** for bond investors who pay attention.

**The Term Spread**

The bottom line measures yield differences between the 10-year and 90-day **Treasury Securities**. Notice that it has gone **negative** four times since 1970. After each instance interest rates **dropped**.

Bond Rating Agencies Are the Bullies of Wall Street

07:29

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How Bond Portfolio Management Could Help Your Active Equity Investment Returns
3 Lectures
16:39

**Interest Rate Risk**

A big part of the risk of bond investing involves interest rate **sensitivity**. First understand that bond prices and yields are **inversely **related.

Bonds with higher **yield to maturity (YTM) **undergo smaller price decreases when rates rise as compared to YTM increases when rates fall an equal magnitude. Long-term bond prices are more **sensitive **to interest rate changes than short-term bonds.

As maturity increases, the sensitivity of bond prices to falling yield, increases at a **decreasing **rate.

**More Interest Rate Sensitivity**

Interest rate risk is inversely related to the bond’s **coupon **rate. Low-coupon bonds are **more **sensitive to interest rates.

The **current **yield to maturity is inversely related to the sensitivity of a bond’s price-to-yield.

Work by Princeton economist **Burton Malkiel** in 1962 shows that all four bonds in this graphic suffer price reductions as yields rise. Furthermore, this relationship is **convex**. Bond prices and yields are **inversely **related.

An increase in yield to maturity induces **smaller **price changes than a decrease of equal magnitude.

The **longer **maturity bond B is more sensitive to interest rate changes than the shorter maturity bond A. Bond B has 6 **times **the maturity of bond A but has less than 6 times the interest rate sensitivity.

This shows that the sensitivity of bond prices to **fluctuations **in yield increases at a decreasing rate as maturity is lengthened.

Bonds B and C are **identical **except for coupon rate. The lower coupon bond is **more **price sensitive to interest rates.

Bonds C and D are the same **except **for yield to maturity. Bond C has the higher yield to maturity and is less **sensitive **to fluctuations in yield. Economists **Homer **and **Leibowitz **in 1972 showed that price sensitivity is inversely related to yield to maturity.

This table gives pricing for 8% Annual **Coupon **bonds at different yields and times to maturity paying just once a year — to simplify. Short term bonds fall by less than 1% on a rate **increase **from 8 to 9%. The 10-year bond price falls more than 6%. The 20-year bond **falls **more than 9%.

Prices fluctuate much more **extremely **when the asset is a zero-coupon bond. The two bonds are not **comparable**.

In fact, we can look at each bond as a portfolio of interest **payments**.

The **annual **coupon bond makes many payments over 10 or 20 years. The zero pays just **once**. This dramatically affects **pricing**.

Here is **why**.

High coupon bonds have more value tied to **payments**; rather than final par value. These have lower **effective **maturities that are some sort of average of all the cash flows.

This is the reason that price **sensitivity **drops with rising coupon rates as Malkiel explained in his fifth rule.

But a higher yield **reduces **the present value of all the bond’s payments, and much more so for those most distant in time. At higher yields the bond value is weighted more **heavily **on earlier payments with lower effective maturity.

This explains why the sensitivity of bond prices to yield fluctuations is **lower**.

With zeros, the situation is the **opposite**. Much more value is **paid **to the final par payment.

The zero-coupon bond is much more interest rate **sensitive**. Higher yield bonds have more weight on **prior **payments which have lower maturity.

**Macaulay’s Duration**

Duration was formulated by economist **Frederick Macaulay**. He published a massive study on railroad bonds in 1938 for the **National Bureau of Economic Research (NBER)**.

**Macaulay’s duration** measures effective bond maturity.

I mentioned this before so that you would understand the **importance **of correctly measuring effective maturity to gauge bond pricing fluctuations based on the 5 +1 rules of Malkiel, et. al. This represents the weighted **average **of the times until each payment, with weights proportional to the present value of the coupon.

You can see that each cash flow is **discounted **and proportional to the bond price. This is **multiplied **by the time to maturity and summed over coupon and par payments as follows.

**The Calculation of the Duration of Two Bonds**

This spreadsheet shows the calculation of the **durations **of two bonds, a zero and an 8% coupon. The assumption is that bond **yield to maturity** is 10%.

The **discount **factor is ten percent.

**Column **E shows the weight and D shows payment present value. Column F is the **product **of weight and payment. This gives us the **values **needed to crunch the duration formula by adding the numbers to column F.

Notice that the **duration **of the zero-coupon bond is 3.0000 years. Duration is the zero-coupon bond’s **maturity**.

This makes sense since the zero-coupon bond only makes one **payment **at par.

The **three-year coupon bond **makes very few payments yet these have an impact on duration. Duration is shorter than the three-year maturity at **2.7774 **years. **Spreadsheets **such as this allow you to change values to make scenario analysis as to how your bond portfolio will fluctuate under different conditions.

Here are the **formulas **you need to set this spreadsheet up yourself in excel.

**Modified Duration**

The rate of change of the yield to maturity of the bond price can be measured as **modified duration**.

**How to Calculate Duration**

Use this spreadsheet to **confirm **the duration of the 8% bond example. **Settlement **date is todays date and the maturity are entered in cells B2 and B3 with the Excel date function. **DATE**(year, month, day). There is no specific date of settlement for this **three-year bond**.

It is **arbitrarily **set with a maturity exactly 3 years later.

Coupon rate and yield to maturity are in **decimal **format. Payment **periods **go into cell 6. **Macaulay **and modified duration results are displayed in cells B9 and B10 as 2.7774 and 2.5249.

**What Influences Duration?**

The easiest way to see what **factors **influence duration is by noticing that a zero-coupon bond’s duration is the time to maturity. This is not so with a **coupon **bond.

With **time **and yield to maturity constant, the bond’s duration and interest-rate sensitivity is higher when the coupon price is lower.

When the coupon **rate **is held constant, the bond’s duration and interest-rate sensitivity generally increases with time to maturity. Here we see that at or above par bonds have increases in duration that are **concomitant **with longer maturity.

Both the **duration **and the interest rate sensitivity of the coupon is higher when the bond yield to maturity is lower. This allows us to set up the **formula **for calculating the level of duration of a perpetuity.

**Perpetuity **Duration= (1+y)/y

Now we can use this to graph the duration as a function of maturity to see **Malkiel’s bond pricing rules**. The plot of the zero-coupon bond shows that the duration is the same as the yield to maturity — this is **rule **1.

The fact that the line of the **three-year coupon bond** is below that of the zero-coupon bond shows that interest rate sensitivity is higher the lower the coupon payment all else equal — this is **rule **2. The plot of the 3% coupon is above that of the 15% coupon bond with equal yields to maturity showing that duration and interest rate sensitivity increases with maturity — this is **rule **3.

The two 15% coupon bonds with **different **yields to maturity have different durations. This illustrates rule 4 that duration and interest rate sensitivity of a coupon bond are **higher **when the bond’s yield to maturity is lower.

In practice, you will see a wide **range **of durations values for actively traded bonds as an investor. This **table **show durations for several coupon bonds all paying 6% per year. Duration decreases with decreasing coupon rates and **increases **with time to maturity. The 20-yer **bond **would fall 1.15% with a rate increase from 6 to 6.1% (= -12.158 X .1%/1.06) but the 5-year bond duration drops just 0.41% (=-4.342 X .1%/1.06). With a **perpetuity **duration is independent of coupon rate.

Are Bond Risks Part of a Right-Wing Conspiracy?

08:39

**Passive Bond Management**

Immunization is a **defense **strategy to shield net worth from interest rate movements. This involves **rebalancing **through periodic portfolio realignment.

**Terminal Value of a Bond Portfolio after Five Years**

Immunization makes a lot of sense for any institution that has bond **obligations **to pay. The idea was developed by **Frank Redington** in 1952 who was a practicing insurance actuary.

**Immunization **allows duration matched assets and liabilities to fully fund an investment portfolio despite adverse interest rate movements.

This table shows that if **interest **rates stay at 8%, that the **funds **from the bond will grow to a $14,693.28 obligation for the issuer in five years. Imagine that an **insurance **company funds this obligation with $10,000 of 8% annual coupon bonds.

These are selling at par value with a 6-year **maturity**.

If market rates continue at 8% there is no **problem**. Both bonds will have an equal **terminal **value.

If interest rates rise, the insurance company faces a **shortfall **to pay the bond investor. Panels B and C show this scenario under duration **matching**.

Panel B shows that a small **surplus **of $0.77 will accrue if rates fall to 7%. Panel C shows that the surplus would be $2.74 should interest rates **rise **to 9%.

Duration matching balances the **accumulated **value of the fixed payments with the sale value of the bond.

**Growth of Invested Funds**

The solid **line **traces the value of bonds if rates stay at 8%. The dashed **curve **represents the value if rates increase. Remember that the issuer faces risk from rate increases; not decreases. The initial **shock **causes a loss. This is recovered by a faster **growth **rate of reinvested funds.

Inflows and outflows **cancel **at maturity in 5 years.

**Market Value Balance Sheets**

This is a balance sheet for the **hypothetical **insurance company in this example. Both assets and **obligations **are valued at $10,000 in panel A. This indicates that the plan is fully **funded**. Panels B and C show that regardless of whether the rate **change **is positive or negative that assets and liabilities change by virtually identical amounts.

**Immunization **is displayed in this graph. At 8% the coupon bond fully funds the obligation where the two present value curves are **tangent **to one another. This is **true **even for small rate changes. This also shows that immunization requires **rebalancing**. At 7% the duration is 5.02 years. It is 4.97 at 9%. Without rebalancing the portfolio durations will not be **matched**. Duration changes with the passage of **time**. Immunization is not a **passive **strategy except for the fact that the manager is not trying to identify undervalued bonds.

**Cash Flow Matching and Deduction**

Cash flow matching involves matching cash flows from a fixed-income portfolio with those of the **obligation**. This is an **immunization **strategy. Multi-period cash flow matching is a **dedication **strategy. This dedicates a **zero **or coupon bond to each cash flow. This **eliminates **interest rate risk once and for all since each cash flow is matched. A dedicated portfolio will **pay **in full no matter the change in interest rates.

**Convexity**

The **curvature **in the bond price to yield is expressed by …

- ∆P/P= -D^* ∆y+1/2 (Convexity) (∆y)^2

The last term arises from a **Taylor **expansion of the modified duration equation. The additional **term **represents convexity. Investors **love **convexity because bonds with greater curvature gain more when yields fall but lose less when rates rise. But the market prices convexity since it is **desirable**. Investor pay **more **and get lower yields on bonds with greater convexity.

**Bond Price Convexity**

This graph shows that the **percentage **change in the bond price is a convex function of the change in yield to maturity. The straight line is the percentage price change **predicted **by the duration rule for a 30 year, 8% coupon bond selling at an initial yield of 8%. The modified duration of the bond at its initial yield is 11.26 years.

The straight line is a plot of **-D*Δy = -11.26 X Δy**.

This indicates that small changes in interest rates have **little **effect on duration. But the duration approximation (straight line) **underestimates **duration. The **true **price and yield relationship is the upward curved (convex) line.

This shows that the duration approximation can become very **inaccurate **for large interest rate changes.

**Why Do Investors Like Convexity?**

More convexity means greater price increases when the market is **good**. But the bond investor **endures **smaller losses when interest rates movements induce a reduction in bond portfolio value.

**Active Bond Management Potential Profit Sources**

The Substitution swap is an **exchange **of one bond for a bond with similar attributes but better pricing.

An inter-market swap switches from one segment of the bond market to another. Rate **anticipation **swap switching is made in response to forecasts of interest rate changes.

**More Active Strategies**

Pure yield **pickup **swaps move to higher yield bonds, usually with longer maturities. Tax swaps entail swapping two similar bonds to receive a **tax **benefit.

Horizon analysis is a **forecast **of bond returns based largely on the prediction of the yield curve slope at the end of an investment horizon.

**Active Fixed-Income Investment Strategy**

For the **strategy **to work …

information cannot already be **embedded **in bond prices to be of value.

Making big **bets **on interest rate movements is unwise except during the rare periods when the yield curve slope is highly negative.

If the manager believes markets are **efficient **they will use substitution swaps and inter-market spreads rather than try to identify undervalued securities.

**Active Bond Speculative Strategies. **

Bill Gross made a **fortune **for his investors betting on the inverted yield curve in bonds. Other bond portfolio managers attempt to identify **undervalued **securities.

This was explained to me by **successful **bond trader Ben Eiler. Ben is a regular on **CNBC**.

An example he gave was a bond series in a **state**. He knew that the person in charge of the **municipal **bonds was not financially sophisticated.

Ben bought the bonds at a cheap **discount**.

He knew that the price would soar when the state **governor **announced that he had assembled a task force to clean up the administration of the municipal bonds. That is because such task forces are composed of the **brightest **and the best in finance from top business schools.

They came in and **cleaned **house. Ben made a sizeable **profit **for his investors as the price rose. Hence, one way you can use what you have learned from this course is to attempt to find **underpriced **bonds.

This course gives you the **tools **to manage your own bond portfolio as a passive or active investor.

Keep in **touch **with me if you do. I want to **know **what happens. **-Doc Brown**

How Duration Could Make you a Better Bond Investor

07:36

Bonus Lecture: My Special Udemy Coupon Offer to You

00:24

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About the Instructor

Major State University Finance Professor, Investments Expert

**"***There is no one like you that I know of who is this transparent, that is what makes your service and education so valuable. Please keep on." -L.B. A Washington State Stock Investor*

**Dr. Scott Brown and “Intelligent Investing” — helping you get the most out of your hard earned investment capital.**

As an **investor**, I have spent over **35 years** reading anecdotal accounts of the greatest investors and traders in history. My net worth has grown **dramatically** by applying the distilled wisdom of past giants.

I have **researched** and tested what works in the world’s most challenging **capital markets** — and I teach you every trick I know in my **Udemy courses**!

**>>>**Learn from **leading financial** **experts**!

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**Enroll**in my Udemy courses — you can **prosper** from all of this — plus much, much more now!

*(In the last six years we have exploded our net worth and are absolutely debt free, we live a semi-retired Caribbean**lifestyle in a**triple gated**upscale planned community from a spacious low maintenance condo looking down on our tropical beach paradise below).*

**My Curriculum Vitae:**

**Investment Writing and Speaking:**

I am an *international***speaker on****investments**** .** In 2010 I gave a series of lectures onboard Brilliance of the Seas as a guest speaker on their

On day 6 the topic I discussed was “** Free and Clear: Secrets of Safely Investing in Real Estate!**“ The day 7 topic was “

**Gina Verteouris** is the **Cruise Programs Administrator** of the **Brilliance of the Seas** of **Royal Caribbean Cruise Lines**. Regarding my **on-board teachings** she writes on June 19th, “*You have really gone above and beyond expectations with your lectures and we have received many positive comments from our Guests*.”

I sponsored and organized an investing conference at **Caesars Palace** in Las Vegas in 2011 under my Wallet Doctor brand. This **intimate conference** was attended by 14 paying attendees.

As such **many strides were made in financial education** that week. For instance I met a woman who is a **retired engineer** from the Reno, Nevada area.

She made a fortune on deep in the money calls during the **bull markets** of the 90s.

This humble and retired engineer inspired me to look more seriously at **deep in the money calls** with far expiration. She also gave me an **important clue** regarding trading volume.

Her call option and volume insights have been confirmed in the **Journal of Finance**.

In 2012 I gave a workshop at the **FreedomFest Global Financial Summit** on stock investing at the **Atlantis Bahamas Resort**. I was also a **panelist** on a discussion of capital markets.

My course “*How to Build a Million Dollar Portfolio from Scratch*" at the **Oxford Club** is an international bestseller. In 2014 I co-authored “*Tax Advantaged Wealth*” with leading IRS expert Jack Cohen, CPA. This was the crown jewel of the **Oxford Club Wealth Survival Summit**.

I have been a regular speaker at the **Investment U Conferences**.

In 2012 I gave a workshop entitled “** How to Increase Oxford Club Newsletter Returns by 10 Fold!**” The conference was held at the

In 2013 I spoke at the Oxford Club’s Investment U Conference in San Diego California. The talk was entitled “** The Best Buy Signal in 103 Years!**” Later in the summer I spoke at the

This was at the same time that **Jimmy Kimmel** married **Molly McNearney** in the posh California celebrity resort. It was fun to watch some of the **celebrities** who lingered.

I also operate a **live weekly investment mentorship subscription** service under the Bullet-Proof brand every Monday night by **GoToWebinar**.

**Academic Research:**

I am an *associate professor of finance* of the AACSB Accredited Graduate School of Business at the **University of Puerto Rico**. My research appears in some of the most prestigious academic journals in the field of investments including the **Journal of Financial Research** and **Financial Management**. This work is highly regarded on both Main Street and Wall Street. My research on investment newsletter returns was considered so important to investors that it was featured in the **CFA Digest**.

The **Certified Financial Analyst (CFA)**is the most prestigious practitioner credential in investments on Wall Street.

Prestigious finance professor **Bill Christie** of the **Owen School of Business** of Vanderbilt University and then editor of **Financial Management** felt that our study was valuable to financial society. We showed that the **average investment newsletter** is not worth the cost of subscription.

I am the lead researcher on the Puerto Rico Act 20 and 22 job **impact** study. This was signed between **DDEC** secretary Alberto Bacó and Chancellor Severino of the University of Puerto Rico.

*(See Brown, S., Cao-Alvira, J. & Powers, E. (2013). Do Investment Newsletters Move Markets? Financial Management, Vol. XXXXII, (2), 315-338. And see Brown, S., Powers, E., & Koch, T. (2009). Slippage and the Choice of Market or Limit orders in Futures Trading. Journal of Financial Research, Vol. XXXII (3), 305-309)*

**Graduate Degrees:**

I hold a *Ph.D. in Finance* from the AACSB Accredited Darla Moore School of Business of the **University of South Carolina**. My dissertation on **futures market slippage** was sponsored by **The Chicago Board of Trade**. **Eric Powers**, **Tim Koch**, and **Glenn Harrison** composed my dissertation committee. Professor Powers holds his Ph.D. in finance from the **Sloan School of Business** at the Massachusetts Institute of Technology [MIT]. Eric is a leading researcher in **corporate finance** and is a thought leader in spin offs and carve outs.

Dr. Harrison is the **C.V. Starr** economics professor at the **J. Mack Robinson School of Business** at **Georgia State University**.

He holds his doctorate in economics from the **University of California at Los Angeles**. Glenn is a thought leader in **experimental economics** and is the director of the **Center for the Economic Analysis of Risk**.

Tim Koch is a professor of **banking**. Dr. Koch holds his Ph.D. in finance from **Purdue University** and is a major influence in the industry.

My dissertation proved that under normal conditions traders and investors are better off entering on **market **while protectingwith **stop limit orders**. The subsequent article was published in the prestigious **Journal of Financial Research** now domiciled at **Texas Tech University** — a leading research institution.

I earned a *masters in international financial management* from the **Thunderbird American Graduate School of International Business**. Thunderbird consistently ranks as the #1 international business school in the **U.S. News & World Report**, and **Bloomberg****BusinessWeek**.

**Academic Conferences:**

I spoke at the 2010 annual conference of the **International Association of Business and Economics (IABE)** conference in Las Vegas, Nevada. The **research** presented facts regarding price changes as orders flow increases in the stock market by **advisory services**.

I spoke at the 2010 **Financial Management Association [FMA]** annual conference in New York on investment newsletters. The paper was later published in the prestigious journal “Financial Management.”

I presented an important study named “* Do Investment Newsletters Move Markets?*” at the

I spoke at the **Clute International Conferences** in 2011 in Las Vegas, Nevada. The research dealt with the price impact of **newsletter recommendations** in the stock market.

I presented a working paper entitled “** The Life Cycle of Make-whole Call Provision**s” at the 2013 Annual Meeting of the

That same year I presented the same study to the Annual Meeting of the **Financial Management Association** in Chicago, Illinois. I did so in session 183 – Topics in Mergers and Acquisitions chaired by James Conover of the University of North Texas with Teresa Conover as discussant. I **chaired** session 075 – Financial Crisis: Bank Debt Issuance and Fund Allocation. Then I was the discussant for **TARP** **Funds Distribution: Evidence from Bank Internal Capital Markets** by **Elisabeta Pana** of **Illinois Wesleyan University** and **Tarun Mukherjee** of the **University of New Orleans**.

**Academic Service:**

I am a member of the **MBA Curriculum Review** Committee, the **MBA Admissions** Committee, The **Doctoral Finance Admissions** Committee, the **Graduate School Personnel** Committee, and the **Doctoral Program** Committee of the School of Business of the University of Puerto Rico.

**Financial Journalism:**

I am the **editor** of Momentum Investor Magazine. I co-founded the **magazine** with publisher **Daniel Hall, J.D.** We have published three issues so far. **Momentum Investor Magazine** allows me to interview very important people in the finance industry. I interview sub director Suarez of the **DDEC** responsible for the assignment of Puerto Rico act 20 and 22 licenses for corporate and portfolio tax reduction in the third edition. Then I interview renowned value investor **Mohnish Prabia** in the upcoming fourth edition — to be made available via Udemy. Valuable stock market **information** will be taught throughout.

**Charity:**

In October of 2010 I arranged for the **donation** to The **Graduate School of Business of the University of Puerto Rico **of $67,248 worth of financial software to the department that has been used in different courses. This was graciously awarded by **Gecko Software**.

I have **guided thousands of investors** to superior returns. I very much look forward to **mentoring** you as to **managing your investments** to your **optima**! **–Scott**

**Dr. Scott Brown**, *Associate Professor of Finance of the AACSB Accredited Graduate School of Business of the University of Puerto Rico.*

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