FIXED INCOME ANALYSIS

In this lesson, we’re going to start tackling the quantitative aspects of bond valuation, in particular, we’re going to see  discounted cash flow analysis, which is the cornerstone of finance, especially for valuation methods. First. We’re going to use Excel to build the BASIC model that helps us see the relationship between the “time value of money” and bond pricing.  We’ll need two elements, basically this is what we need all the time, [1] the future cash flows and when they occur, and [2] the appropriate  discount rate to calculate their present value. The pricing of bonds revolves around the formula of discounted cash flow analysis. Using Excel, we’ll use the DCF formula to make some simple calculations.

In this lecture, we’re going to delve a little deeper into the mechanics of yield-to-maturity, which is a fundamental tool in fixed income analysis. Actually, this lesson is not going to cover all things yield-to-maturity, because this is a tool, a concept that it’s going to stay with us for long. We'll add details about this important tool throughout the other following lessons, because we’re going to keep seeing yield-to-maturity pop up time and again and we’re going to keep using it until the end of this course.

In this lecture we’ll deal with how interest is calculated, because when a seller sells a bond between two coupon dates the buyer agrees to pay the interest accrued between the last coupon payment date and the settlement date which is usually the second business day following the trade date; we’re going differentiate between flat and full price and at last we’re going to illustrate the difference between the two primary conventions for day count in calculating accrued interest for a bond, we’ll be referring implicitly to a modified equation that we'll use to compute the present values by taking into account the fraction of time in between two coupon dates.

In this lesson we’re going to talk about a bond’s price/yield relationship and its featuring elements: yield, coupon, convexity and time to maturity and the pull-to-par effect: the constant yield price trajectory as time passes by. We’ll be basically looking at our general equation for pricing a bond, as we’ve already seen, in one of our first lessons.

In this video we’re going to talk about periodicities and annualised yields and we’re going to elaborate with regard to effective annual rates, how periodicity affects them, what we should do for zero coupon bonds, and at last the convention for conveying bond yields called bond equivalent basis, and we’ll be using this formula for periodicity or compounding conversions.

In this lesson we’re going to talk about some measures of yield-to-maturity suitable for bonds with embedded options. A callable bond gives the issuer the right to recall, hence callable, the bond from investors at specific prices and during pre-determined periods after an initial period called protection period when the issuer cannot exercise the option to buy back the bond. The callable provision is probably the most common, together with the convertible one, embedded option found in bond instruments. It’s embedded because it can’t be traded separately from the bond, it is an option, and as some of you may know options are traded in financial markets, but in this case it can’t be traded separately. Moreover, we’re also going to talk about other common measures of yield for bonds.

In this lecture we’re going to see why it’s important to understand why bond prices and yields-to-maturity change: to do this it’s necessary to split a yield-to-maturity into a base rate, or benchmark rate, and an issuer specific spread. In this lesson, we’re going to see three commonly used measures of spread for bonds: G-spread, I-spread and Z-spread. On a popular tool, in many investment banks, asset management firms and securities brokers, like Bloomberg, you can see these common spread measures that are commonly expressed in basis points.

In this lesson, we’ll distinguish between the quoted margin and the required margin and we’ll calculate the second, the required margin using an Excel’s add-in called SOLVER. Solver will do what GOAL SEEK does and much more, and it’s worthwhile taking a look at it because it’s very powerful. The basic formula we used in one of our previous lessons is the one we used to price a bond on a coupon date, we can still use it, though in a modified version to deal with floating rate bonds.

In this lesson, more in general in this section, we want to learn more about the relationship between maturity and interest rates, more specifically, spot, forward and par rates. There’s a relationship among these rates: spot, forward and par rates and we’re going to study it. We're going to extract zero rates from traded prices and we're also going to introduce the shape of the yield curve.

In this lecture we’re going to see what par and forward rates are: they’re also related to maturity, it’s just that they’re different from spot rates and they have similar as well as differing uses. In fixed income analysis, a par rate is the theoretical yield on a fixed-income security, assuming its market price is equal to its par value. First of all, par rates helps understand how much interest a bond needs to offer to be sold at par value initially. It essentially reflects the market's required return for holding a bond with a specific maturity. Par rates derived from theoretical government bonds with different maturities are used in fixed income analysis because by taking into account tax and other trading distortions in actual bonds that are priced at discount or premium. The par rate serves as a reference point for issuers to determine the appropriate coupon rate for a new bond issue and reflects the minimum interest rate that investors would require to be enticed to buy a bond with a specific maturity, given the current market interest rates for bonds of similar risk and credit quality. The par rate, or par yield, serves as a vital reference point for issuers when they decide on the coupon rate to offer on a new bond to be competitive in the market.

In this lesson we also dive into the world of interest rate dynamics and the yield curve. We’ll explore the theories that try and explain why the yield curve shifts, changes steepness, or modifies its curvature. These movements are driven by key economic variables and market events, impacting bond pricing and required returns.

We'll talk about the bond risk premium, which is the extra return you get from holding a long-term bond over a short-term one. This premium is influenced by factors like inflation, economic growth, and monetary policy. For instance, central banks, like the ECB, tweak interest rates to control inflation and promote economic growth, which in turn affects bond yields.

Fiscal policy, investor demand, and market uncertainty also play big roles. When markets are shaky, investors often flock to government bonds, causing yield curves to flatten. We’ll also discuss how fixed-income traders use interest rate forecasts to shape their portfolios, whether by adjusting duration or engaging in strategic bond trades. Lastly, we’ll cover explicitly the theories that explain the shape of the yield curve, such as the Expectations Theory and the Liquidity Preference Theory.

In this lesson we’re going to see that bond investors have three sources of return: first; coupon payments, the periodic interest payments made by the bond issuer to the bondholder and the face value at redemption; second, capital gains (or losses): if the bond is sold before maturity, the investor can realise a capital gain if the bond’s price has increased since purchase or a capital loss if the price has decreased; and third, reinvestment income: this is the return generated from reinvesting the coupon payments received. The total return on a bond investment can be affected by the rate at which these coupon payments are reinvested. Reinvestment income assumes that the investor reinvests the coupon payments at the prevailing interest rates.

In this lesson we’re going to see investment horizon, reinvestment risk and price risk affect one another by introducing an important consideration that revolves around a useful quantity: Macaulay's duration, or simply duration.

In this lesson Macaulay’s duration is used as an investment horizon strategy to match a bond portfolio's duration with the investor's time horizon. By doing so, investors can minimise interest rate risk, as price risk and reinvestment risk offset each other. This strategy ensures that the investor's returns are less affected by fluctuations in interest rates, providing a more stable and predictable outcome over the specified holding period. It’s called Macaulay’s duration after the Canadian economist that developed this measure almost 100 years ago. It’s often referred to as simply duration. We’ll refer to a fixed-rate bond to demonstrate that Macaulay’s duration is the weighted average of the time to receipt of the bond’s cash flows.

In this lesson, we’re going to see how this metric helps investors understand the bond's sensitivity to interest rate changes, with longer durations indicating higher sensitivity.

Understanding Macaulay duration enables investors to better assess bond investments and align them with their risk tolerance and investment horizon: because from Macaulay duration we can derive modified duration that is the MOSTLY USED METRIC for interest rate risk, together with MONEY DURATION and the PRICE VALUE OF A BASIS POINT. We already saw that the price of a bond is inversely related with its yield-to-maturity: in this video we’re going to start QUANTIFYING, MEASURING, this relationship.

In this lesson, we’re going to explore further the relationship between interest rate changes and a bond’s price. Building on modified duration, in this video we'll introduce convexity, which refines this understanding by accounting for the curvature in the price-yield relationship. While duration estimates the linear price change, convexity captures the non-linear effect, providing a more accurate prediction of price movements, especially for larger interest rate shifts: we'll estimate the price change for a bond by taking into account a convexity adjustment.