Question

7. Using historical data to measure portfolio risk and correlation coefficient Aa Aa Pam is an investor who believes that past variability of stocks is a reasonably good estimate of future risk associated with the stocks. Pam works on creating a new portfolio and has already purchased stock A. Now she considers two other stocks, B and C. Pam collected data on the historic rates of return for all three stocks, which are presented in the following table. Complete the table by calculating standard deviations for each stock: Year Stock A Stock B Stock C 2013 40% -5% 35% 2014 -10% 40% -5% 35% -10% 2015 -10% 2016 -5% 35% 40% % % Average return Standard deviation Suppose Pam can only afford to complement stock A by adding just one of the two other stocks, either stock B or stock C. Complete the following table by computing correlation coefficients between stocks A and B and between stocks A and C, and calculate average returns and standard deviation for the two potential portfolios, AB and AC: Stocks A and B Stocks A and C Correlation coefficient Average return % Standard deviation

I ONLY CAN SHOW ONE OPTIONS OF THEM

Answer 1

1.

average return = sum of all returns / number of terms

For stock A,

average return = (40 - 10 +35 - 5) / 4 = 15%

Standard deviation=

data	data-mean	(data - mean)2
40	25	625
-10	-25	625
35	20	400
-5	-20	400

2 Σ-)- 2050 2 Σ-) 205026.1406 4-1 σ n- 1

For Stock B and Stock C, since the values are same (just the order is different) So mean and Standard deviation will remain same.

MEAN=15%

SD=26.14

2.

(a) STOCK A AND B

CORRELATION COEFFICIENT:-

X	Y	X⋅Y	X⋅X	Y⋅Y
40	-5	-200	1600	25
-10	40	-400	100	1600
35	-10	-350	1225	100
-5	35	-175	25	1225

∑X=60 , ∑Y=60 , ∑X⋅Y=−1125 , ∑X2=2950 , ∑Y2=2950

ΣΧΥ- Σx. ΣΥ η. Τ VΗΣΧ-ΣxΣΥ-Συ] 4. 1125 60 60 --0.9878 Τ |4- 2950 - 602 | V4- 2950 602

AVERAGE RETURN-

Since weight of stock A and B is same (i.e. 0.5 each) So average return is the average of stock A and B i.e. 15%

STANDARD DEVIATION of PORTFOLIO:-

Op (WA2Ag2 o22wAwBooBPAB)1/ 2 +

here W_A = W_B = 0.5

SD of A = SD of B = 26.1406

Rho is the correlation coefficient calculated above = -0.9878

So SD of portfolio comes out to be 2.04

Similarly for portfolio A and C

X	Y	X⋅Y	X⋅X	Y⋅Y
40	35	1400	1600	1225
-10	-5	50	100	25
35	-10	-350	1225	100
-5	40	-200	25	1600

∑X=60 , ∑Y=60 , ∑X⋅Y=900 , ∑X2=2950 , ∑Y2=2950

n. ΣΧΥ-ΣΧ. ΣΥ Τ VIΣΧ-(Σx.ΣΥ- Σ ηi] 4-900 60 60 Τ 4.2050-602 4-2950- 60|

AVERAGE RETURN-

Since weight of stock A and B is same (i.e. 0.5 each) So average return is the average of stock A and B i.e. 15%

STANDARD DEVIATION of PORTFOLIO:-

As above, it is 18.48

3.

Portfolio AB, it has lower standard deviation and negative correlation coefficient

4.

Diversification can reduce risk but not eliminate it
Returns on stocks in the same industry are more closely correlated than on stocks in different industries