Bond valuation
Bond Valuation and Analysis in R
Clifford Ang
Senior Vice President, Compass Lexecon
Bond valuation
- Fixed annual coupon rate
- Fixed maturity date
- Option-free
Value of an asset
- The value of an asset = present value of expected future cash flows
- Cash flows: discounted at the appropriate risk-adjusted discount rate
$$
$$V = \sum_{t=1}^{T} \frac{CF_t}{(1+y)^t}$$
$CF$: cash flows
$y$: discount rate
Laying out a bond's cash flows
- Prior to maturity, the investor receives coupon payments
$$\sum_{t=1}^{T-1} \frac{CF_t}{(1+y)^t}$$
- NB: sum up to $T-1$
- At maturity, the investor receives the last coupon payment and the par value
$$V = \sum_{t=1}^{T-1} \frac{CF_t}{(1+y)^t} + \frac{C_T + P}{(1+y)^T}$$
Creating a cash flow vector
$$
$$V = \sum_{t=1}^{T} \frac{CF_t}{(1+y)^t} + \frac{C_T + P}{(1+y)^T}$$
$$
cf <- c(c1, c2, c3, c4, c5, ...)
Converting to dataframe
- So we can add additional columns, we need to convert the cash flow vector into a data frame
- Use the
data.frame()commandcf <- data.frame(cf)
Creating a time index
- Each cash flow occurs at a certain period of time
- The unit of the periods will be in years
- We create a variable that creates a time index
cf$t <- c(1, 2, 3, 4, 5, ...)
Calculating the PV factors
- To discount the cash flows, we need a "discount rate"
- For bonds, the discount rate is called a "yield"
- We create a present value factor used for discounting
cf$pv_factor <- 1 / (1 + y)^cf$t
pv_factor <- 1 / (1 + .10)^2
pv_factor
0.8264463
PV of cash flows
- We calculate each cash flow's present value
cf$pv <- cf$cf * cf$pv_factor
- The sum of the present values of the bond's cash flow is equal to the bond's value
sum(cf$pv)
Let's practice!
Bond Valuation and Analysis in R
