Question

(a) You invest $27,000 in a corporate bond selling for $900 per $1,000 par value. Over the coming year, the bond will pay interest of $75 per $1,000 of par value. The price of the bond at year’s end will depend on the level of interest rates that will prevail at that time. You construct the following scenario analysis:

Interest rate	Probability	Year-end bond price
High	0.20	$850
Unchanged	0.50	$915
Low	0.30	$985

Your alternative investment is a T-bill that yields a sure rate of return of 5%.
(i)            Calculate the holding period return (HPR) for each scenario
(ii)           Calculate the expected rate of return, and the risk premium on your investment.
  
(b) You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client’s portfolio?

Answer 1

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Answer:

i)

HPR = (Interest + Closing price - Purchase price) / Purchase price

High = (75 + 850 - 900) / 900

= 2.78%

Unchanged = (75 + 915 - 900) / 900

= 10%

Low = (75 + 985 - 900) / 900

= 17.78%

ii)

Expected rate of return = Sum of (return * Probability)

= (2.78% * .2 + 10%*.5 + 17.78%*.3)

= 10.89%

Risk premium = Expected return - T bill rate

= 10.89% - 5%

= 5.89%

Expected end-of-year dollar value of your investment = Sum of (Price * Probability)

= (850*.2 + 915*.5 + 985*.3)

= 923

b)

Expected return on an equity fund is the sum of expected risk premium and rate on t-bills.

Therefore,

E(R) = 10% + 6% = 16%

Excel working: