In: Finance
Expected return of stock Alpha is 8 percent and of stock Beta is 12 percent. The standard deviation of the stocks are 13 percent and 18 percent respectively. The correlation between these two stocks is 0.4. If the portfolio manager has decided to invest all the funds that he holds in some proportion in these two assets. The expected return of the portfolio based on this proportion is 11.5%. What are the weights in each of the stocks? What is the standard deviation of this portfolio?
Portfolio Ret= Weighted Avg Ret of securities in that portfolio.
Let y be the weight inStock Alpha.
Stock | Weight | Ret | WTd Ret |
Stock Alpha | y | 0.0800 | 0.08y |
Stock Beta | 1-y | 0.1200 | 0.12 - 0.12y |
Portfolio Ret Return | 0.12 - 0.04y |
Thus 0.12 - 0.04y = 0.115
0.04y = 0.12 - 0.115
= 0.005
y = 0.005 / 0.04
= 0.125
weight in Stock Alpha = 0.125 I.e 12.5%
Weight in STock Beta = 0.875 I.e 87.5%
Portfolio SD:
It is nothing but volataility of Portfolio. It is calculated
based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual
Asset's SD in portfolio. We can't reduce the SD through
diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at
propoer weights.
If correlation > -1 but <1, We can reduce the SD, n=but it
will not become Zero.
Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B
A = Stock ALpha
B = Stock Beta
Particulars | Amount |
Weight in A | 0.1250 |
Weight in B | 0.8750 |
SD of A | 13.00% |
SD of B | 18.00% |
r(A,B) | 0.4 |
Portfolio SD =
SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.125*0.13)^2)+((0.875*0.18)^2)+2*(0.125*0.13)*(0.875*0.18)*0.4]
=SQRT[((0.01625)^2)+((0.1575)^2)+2*(0.01625)*(0.1575)*0.4]
=SQRT[0.0271]
= 0.1647
= I.e 16.47 %
Portfolio SD is 16.47%