Question

AAA Inc has issued at par a zero-coupon bond with a ten-year maturity. Investors believe there is a 10% chance that AAA will default on these bonds. If they do default, investors expect to receive only 50 cents per dollar they are owned. What is the approximate expected return that investor will earn from this bond, if the bond is trading today at 90 percent of par value? Assume annual compounding.

Answer 1

The given problem can be written as follows -

Scenario (A)	Probability (B)	Future Cash Inflows (C)	(B)*(C)
1. Default	10%	50	5
2. No default	90%	100	90
		TOTAL	95

Now, the investor can expect to get 95 $ (after 10 years) for every 90 $ he invests today.

All we need to find now is the rate at which 95 $ can be discounted over 10 years (annual compounding) to get 90 $ in Present value terms. Using Hit & trial, we get 0.55 % as the rate per annum.

Thus approximate return the investor can expect to earn is 0.55% p.a.