From 0 to 1: Bond Theory and Valuation

Credit is the life-blood of financial markets and has been for centuries. There are various credit instruments available in the market. It is important to understand what credit is and why do people, Government or Corporations require credit.

Before going into details of investments in bonds, knowledge about the issuer of bonds is important. The bonds are usually issued by Government and Corporation. They need to be credit-worthy for people to invest in the bonds. This is given through the Bond Ratings

There are many specific attributes attached to bonds like the issuer, holder, time to maturity, coupon rate, par value, etc. which investors ought to be familiar.

A longer time to maturity for a bond would increase the riskiness of the bond and the issuer needs to compensate the investors for this risk. This would impact the Yield of the bond and the Yield Curve represents the market rates for different bond length

Discounting of Bond and calculating the Yield of a bond

Before investing in bonds, investors need to understand the relationship between various features of bonds. The bond interest is related to bond yield and this decides the relation between Price and Par Value

The bond is accompanies by a coupon rate which can be fixed or floating unless it is a Zero-Coupon bond. Coupon adds to the income of the bond holder but gives rise to reinvestment risk.

Interest Rate risk is the risk that investment value will change with a change in the bond yield. This risk varies for different types of bonds like put and call options

Price-Yield Curve of Bond is a convex graph. Slope of this graph gives the quantum of Yield which gives the sensitivity to interest rate risk. This risk can be measured in terms of Duration

Many bonds contain various options for investors and borrowers like the put or call options, conversion options or the floor interest rates option. These make bonds more attractive and also effect the basic features of bonds.

A simple example to compute interest income, total amount at maturity, bond price, yield and the cash flow statement

One level higher in complexity, compute the accrued interest, clean price all including floating interest rates

Few different concepts explained through examples like bond rating and the relation between interest, yield and price.

We will calculate various attributes of bond given the bond duration and understand the impact of bond duration. We will also calculate the value of put and call options.

Calculate present value of bonds and check if bond is at discount or not

Deriving the Modified Duration and Macauley Duration from the negative relationship between yield and prices

Understanding Modified Duration and Macauley Duration better with examples

Understanding the Zero Coupon bonds and why they are more volatile. We will also understand Error Margins.

To account for error margin in calculating bond price change with a yield change we need bond convexity. The formula for duration needs to include bond convexity to get rid of error margin.

Solve few previous examples using the convexity formula and see how introducing convexity deletes the error margin.

If we have bond prices we can estimate the duration and convexity using finite-difference approximations of derivatives, i.e. Effective Convexity and Effective Duration. This helps in taking buy or sell decision.

The idea of Net Present Value (NPV) is one of the most fundamental in all of finance - and it all starts with compound interest.

NPV and price are related: if NPV > price, the asset is undervalued, and should be bought ASAP! If NPV < price, the asset is overvalued - don't buy it.

Calculate the NPV of a cash flow in the future. The cash flow is deterministic, btw.

Finding out future value of cash put away today using compounding with risk free rate of return.

The higher the compounding frequency on the risk-free instrument, the higher the discount rate.

Taken to its limit, compounding could be continuous. This yields the highest possible discount factor, given a certain discount rate.

Calculating the NPV of a stream of cash flows in the future is one of the most common use-cases in all of finance. Its used across bond math as well as corporate finance.