Question

The following data apply to Computational Problems 7‐1 through 7‐4. Assume expected returns and standard deviations as follows:

EG&G Return (%)   25

Standard deviation (%)   30 Covariance   112.5 The correlation coefficient,

ρ, is 0.15. GF 23 25

EG&G wi 1.0 0.8 0.6 0.2 0.0

GF wj = (1 − wi) 0.0 0.2 0.4 0.8 1.0

(1) Portfolio Expected Returns (%) 25.0 24.6 24.2 23.4 23.0

(2) Variance 900 637 478 472 625

(3) Standard Deviation (%) 30.0 25.2 21.9 21.7 25.0

7‐1   Confirm the expected portfolio returns in column 1.

7‐2   Confirm the expected portfolio variances in column 2.

7‐3   Confirm the expected standard deviations in column 3

. 7‐4   On the basis of these data, determine the lowest risk portfolio.

7‐5   Assume that the risk‐free rate is 7 percent, the estimated return on the market is 12 percent, and the standard deviation of the market’s expected return is 21 percent. Calculate the expected return and risk (standard deviation) for the following portfolios:

a. 60 percent of investable wealth in riskless assets, 40 percent in the market portfolio

b.   150 percent of investable wealth in the market portfolio

c.   100 percent of investable wealth in the market portfolio

Answer 1

And std dev = Variance^1/2

We will now check the results we have obtained.

	EG&G	GJ
Return	25.00	23.00
Std Dev	30.00	25.00
Covariance	112.5	Correlation	0.15
Wi	1	0.8	0.6	0.2	0
Wj = 1 - Wi	0	0.2	0.4	0.8	1
Portfolio Expected returns (%)	25.00	24.60	24.20	23.40	23.00
Variance	900	637	478	472	625
Standard Deviation (%)	30.0	25.2	21.9	21.7	25.0

So, the calculations are correct in 7-1, 7-2 and 7-3

Part 7 - 4

Based on this, the loswest risk corresponds to the portfolio with lowest std dev. This corresponds to the portfolio with 20% of EG&G and 80% on GJ.

Part 7 - 5

(a) E(R) = w x Rf + (1 - w) x Rm = 60% x 7% + 40% x 12% = 9.00%

Std dev = (1 - w) x Std dev of market = 40% x 21% = 8.40%

(b) E(R) = - 50% x Rf + 150% x Rm = -50% x 7% + 150% x 12% = 14.50%

Std dev = 150% x 21% = 31.50%

(c) E(R) = 100% x Rm = 100% x 12% = 12%

Std dev = 21%