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The expected return on Big Time Toys is 11 percent and its standard deviation is 19...

The expected return on Big Time Toys is 11 percent and its standard deviation is 19 percent. The expected return on Chemical Industries is -1 percent and its standard deviation is 23 percent. Suppose the correlation coefficient for the two stocks' returns is 0.8. What are the expected and standard deviation of a portfolio with 70 percent invested in Big Time Toys and the rest in Chemical Industries?

Enter your answers as percentages rounded to 2 decimal places. Do not include the percentage sign in your answers.

E(rp) =

Std. Dev.=

Solutions

Expert Solution

Part A:

Portfolio Ret = Weighted avg ret of securities in that portfolio.

Stock Weight Ret WTd Ret
Big time toys 0.7000 11.00% 7.70%
Cehmical industries 0.3000 -1.00% -0.30%
Portfolio Ret Return 7.40%

Expected Ret is 7.40%

Part B:

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 = Big time toys

B = Chemical company

Particulars Amount
Weight in A 0.7000
Weight in B 0.3000
SD of A 19.00%
SD of B 23.00%
r(A,B) 0.8

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.7*0.19)^2)+((0.3*0.23)^2)+2*(0.7*0.19)*(0.3*0.23)*0.8]
=SQRT[((0.133)^2)+((0.069)^2)+2*(0.133)*(0.069)*0.8]
=SQRT[0.0371]
= 0.1927
= I.e 19.27 %

Portfolio SD is 19.27%

jeff jeffy answered 2 years ago
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