Suppose that a security costs $3,000 today and pays off some amount b in one yea

Question

Suppose that a security costs $3,000 today and pays off some amount b in one year. Suppose that b is uncertain according to the following table of probabilities: b: $3,000 $3,300 $3,600 $3,900 $4,200 Probability: 0.1 0.2 0.3 0.2 0.2

A Calculate the return (in percent) for each value of b. (Note: You may just calculate the total return and not worry about how this is split between current yield and capital-gains yield.)

B Calculate the expected return (in percent).

C Calculate the standard deviation of the return.

D Suppose that an investor has a choice between buying this security or purchasing a different security that also costs $3,000 today but pays off $3,300 with certainty in one year. How is an investor

Explanation / Answer

A)

if it gives 3000 return is 0%

if it gives 3300 return is 10%

if it gives 3600 return is 20%

if it gives 3900 return is 30%

if it gives 4200 return is 40%

B)

expected return is 0.1 * 0 + 0.2 * 10 + 0.3 * 20 + 0.2 * 30 + 0.2 * 40 = 22%

C)

std dev is 12.49%

D)

If the investor is risk averse he prefers the one that pays $3300, if he is risk loving he prefers the security with various payoffs

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