Question

Asset 1 has an expected return of 10% and a standard deviation of 20%. Asset 2 has an expected return of 15% and a standard deviation of 30%. The correlation between the two assets is less than 1.0 i.e., they are not perfectly correlated. You form a portfolio by investing half of your money in asset 1 and half in asset 2. Which of the following best describes the expected return and standard deviation of your portfolio?

		The expected return is between 10% and 15% and the standard deviation is greater than 30%.
		The expected return is 12.5% and the standard deviation is 30%.
		The expected return is 12.5% and the standard deviation is less than 30%.
		The expected return is 12.5% and the standard deviation is greater than 30%.

Answer 1

Ans:- Expected return of the portfolio will be respective weights * respective return

=0.50*10+0.50*15 = 12.50%

The standard deviation of the portfolio will be given by [ W1*SD1+W2*SD2+2*W1*W2*SD1*SD2*r ]^(1/2), where W is weights, SD is the standard deviation, r is the correlation between 1 and 2.

Correlation values always lie between -1 & 1. -1&1 occurs when both the assets are perfectly positive or perfectly negative. Since it is given that both the assets are not perfectly correlated therefore correlation value of both these assets would be between -1 and 1.

Now we will put a few values between -1 & 1 including -1 & 1 and analyze its standard deviation values.

From the above analysis, we see that if both the assets were perfectly negative correlated ( r =-1) or perfectly positive correlated (r =+1) then the SD values would lie between 5% and 25%, but since the assets are not perfectly correlated, therefore its SD value will always lie between 5% and 25%. For example, we if r =-0.50, then SD is 13.23, and if r = 0.75, then SD is 23.45.

Therefore SD will always be less than 30% if we put any values of r (-1<0<1).

So, The expected return is 12.5% and the standard deviation is less than 30%.option (c) is the right answer.

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