Ah Lee, a financial manager at a US based mid-sized manufacturing firm, has been caught off-guard before. In an effort to earn the most on excess cash, Ah Lee once bought five-year US Treasury bonds (a maturity longer than the firms liabilities) only to see interest rates rise. The loss when the Treasury bonds were sold did not make Ah Lees supervisor, Carlo, Chief Financial Officer, very happy.

Ah Lee is now in a similar situation - Carlo has asked for a recommendation on the investment of another $10 million in excess cash.

Risk and Return using RCY

The risk of unexpected changes in interest rates is a given with coupon-paying bonds. Even if the bonds are held to maturity, there is reinvestment risk. A bonds exposure to interest rate risk depends on the size and the number of coupon payments made to the bondholder. The realized return from a bond depends on the rates at which the coupons are invested; the rates can only be estimated at the time the bond is purchased.

Given estimates of futures interest rates, however, the expected realized compound yield (RCY) can be calculated in order to cope with the reinvestment problem. For a bond that pays annual coupons over n years, the appropriate calculation for the annualized return is:

RCY = [(Total future dollar value/Purchase price of bond)1/n - 1].

The total future dollar value from the investment includes the coupon payments, the earnings on each coupon, and the value of the bond at the end of the holding period. In estimating the future dollars from a bond purchase, Ah Lee needs a forecast of the direction and level of future interest rates. At yesterdays investment meeting, Carlo stated his belief that interest rates would remain unchanged for the next three years because of an unchanging expected inflation rate. Ah Cheung, another financial manager at the firm and someone that has earned Carlos respect for his reasoned judgment, suggests Ah Lee use the current term structure to gauge interest rate expectations. He uses the following table from Federal Reserve Statistical Release H.15 to get current spot rates on one-, two-, and three-year constant maturity Treasury securities.

Treasury constant maturities Spot Rate Today

1-year 1.54%

2-year 1.61%

3-year 1.61%

4-year 1.63%

5-year 1.65%

7-year 1.75%

Task

"Carlo will accept a recommendation different than his own only if it is justified by analysis," advises Ah Cheung. "Well-reasoned analysis is an opportunity to gain back some of Carlo trust, which was lost after your last bond purchase."

Ah Lees problem is to recommend the best investment among three different US Treasury bonds. The $10 million investment will be liquidated in three years to help repay a bank loan charging a fixed rate interest at 8.50% per year. The bonds, each with a $1,000 par value and annual convention, are described as following:

Bond 2 Bond 3 11.625% 5 .5% $1403.39 $1107.59

Bond	Annual Coupon	Current Price	Maturity (yrs)
Bond 1	0%	$882.50	5
Bond 2	11.625%	$1403.39	5
Bond 3	5 .5%	$1107.59	3

Note: This is an important recommendation for Ah Lee that can affect his career. Although no one knows the future course of interest rates (not even Carlo), Ah Lee knows it is essential to consider the impact of an unexpected change in interest rates on each of the bonds. To Ah Lee, it is probably least risky to assume Carlos forecast is the best because hell have no one to blame but himself if Ah Lee makes a recommendation based on the forecast.