Question

RISK AND RETURN –

(A) Consider the expected return and standard deviation of these four stocks (chart below). If investors are buying only one stock, which one of these stocks would no investor buy? Why? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL).

STOCK	EXPECTED RETURN	STANDARD DEVIATION
A	6%	1%
B	7%	1.5%
C	7%	2%
D	8%	2%

ADDING AN ASSET TO A PORTFOLIO -

(B) Your current portfolio's cash returns over the past three years look like this:

	YEAR 1	YEAR 2	YEAR 3	E(CF)	o
Your Portfolio CF's	120	100	80	100	20

The past three years are representative of a good year, an average year, and a bad year for you. You are considering adding one of these two equally priced assets to your portfolio:

	YEAR 1	YEAR 2	YEAR 3	E(CF)	o
New Asset 1	6	6	6	6	0
New Asset 2	2	6	10	6	4

Which asset would be best for you? Calculate the portfolio expected return, variance, and standard deviation when adding each new asset? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL).

Answer 1

A) We will calculate coefficient of variation for the four stocks, where coeff. of variation = standard deviation/expected return

STOCK	EXPECTED RETURN	STANDARD DEVIATION	Coeff. Of variation
A	6%	1%	16.67%
B	7%	1.50%	21.43%
C	7%	2%	28.57%
D	8%	2%	25.00%

Now, the lower the coefficient of variation the better it is, as that means that the stock provides same return with a lower standard deviation or risk taken. Hence, we will pick the three stocks with the lowest coeff. of variation first. Hence, no investor would buy Stock C, which has highest coeff. of variation.

B) New Asset 2's returns exhibit exactly opposite movements as compared to the current portfolio, while New Asset 2's returns remain flat.

I will choose New Asset 2, as adding this will diversify the risk of my portfolio, as New Asset 2's returns will smoothen my current portfolio's return performance, by compensating the decline of my current portfolio when my current portfolio is facing a bad year and vice versa in a good year. As the below calculation shows, adding New Asset 2 leads to lower standard deviation while giving the same expected return as compared to the portfolio with New Asset 1

	YEAR 1	YEAR 2	YEAR 3	E(CF)	Variation	Standard Deviation
Existing portfolio CF's	120	100	80	100
New Asset 1	6	6	6	6
New Asset 2	2	6	10	6
New portfolio with asset 1	126	106	86	106	266.67	16.33
New portfolio with asset 2	122	106	90	106	170.67	13.06

Formula used to calculate expected return is AVERAGE, for variance use VARP, for standard deviation use STDEVP