Question #225242

You buy a bond for $1000 today that promises interest of $50 in one year plus the return of your principal. However, the probability that the company will default and not pay you either interest nor repay your principal is 1 percent. The expected return on the bond is ____ percent.

Expert's answer

**Solution:**

The expected value of a bond after one year = Sum (Return x Probability)

Where: Return = Expected return

Probability = Expected probability

Probability of 0.01 will yield $0 expected returns

Probability of 0.99 will yield $1,050 expected returns

The expected value of a bond after one year = (0 "\\times" 0.01) + (1050"\\times" 0.99) = 0 + 1039.5 = "\\$1,039.50"

The expected value of a bond after one year = "\\$1,039.50"

Therefore, the expected return of a bond ="\\frac{1039.50 - 1000}{1000} = 0.0395\\times 100\\% = 3.95 \\%"

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