Question

An investor is considering two portfolios (Portfolio 1 and 2). Both possible portfolios consist of a 50% weight on Asset A: this asset has an expected return of 12% and a standard deviation of 18%. The other half of Portfolio 1 consists of Asset B: it has an expected return of 8% and a standard deviation of 10%. The other half of Portfolio 2 consists of Asset C: it has an expected return of 8% and a standard deviation of 14%. Is it true with certainty that the standard deviation of Portfolio 1 is smaller than the standard deviation of Portfolio 2?

Answer 1

Portfolio SD:

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]

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

Thus Portfolio SD not only depemds on Weight of investment, SD of Investemnt but also Correlation between stocks.

Thus we can't tell certainly, SD of Portfolio 1 is smaller than SD of Portfolio 2.