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Homework answers / question archive / Which of the following statements is True? The standard deviation of a portfolio is always less than or equal to the weighted average of the standard deviations of the assets in the portfolio Both (a) and (b) The minimum variance portfolio constructed from many risky assets is always risk free, The expected return of a portfolio is always less than the weighted average of the expected returns of the assets in the portfolio
Which of the following statements is True? The standard deviation of a portfolio is always less than or equal to the weighted average of the standard deviations of the assets in the portfolio Both (a) and (b) The minimum variance portfolio constructed from many risky assets is always risk free, The expected return of a portfolio is always less than the weighted average of the expected returns of the assets in the portfolio
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.
Thus in any case, portfolio Risk is less than or equal to weighted avg risk of securities in that portfolio.
Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B
At Minimum variance Portfolio, Portfolio risk is minimal. may not be definitely Zero.
Expected Ret of Portfolio is weighted Avg ret of securities in that portfolio.
Hence Statment A alone is correct.
