One approach to calculate the price of the bond is to discount each cash flow by the spot rate corresponding to the time at which the cash flow occurs. The CFAI text works through an example of this and then it proceeds to calculate the YTM for the bond given the price calculated using spot rates.
However, doesn’t calculating the YTM run counter to the idea that each cash flow represents a different level of risk (which is something the spot rate method could suggest) ? How can we simultaneously assume each cash flow has the same level of risk and that each cash flow has a different level of risk?
Let me know if this doesn’t make sense. I can clarify further if it doesn’t.
Cash flows don’t all occur at the same time, that’s why when you discount by spot rates, the spot rates are different. The 1-year rate is not the same as the 2-year rate, the 3-year rate, etc. There is inherent risk with longer maturity bonds, which is why there are different rates for each year.
The YTM should equal the weighted average of the spot rates. Check out this example below, I just made some numbers up for the spot rates on the top example. Then I used YTM to solve for the same bond. These should equal.
Ok yea, this makes sense because the YTM is just a money-weighted rate of return. But why calculate YTM when we already know each cash flow has a different level of risk associated with it by the spot rates? Doesn’t the YTM assume each cash flow has the same level of risk?
