Question

1. You are shown the following data. If the correlation coefficient between the combined portfolio of A+B and C is 0.2, what would happen to the overall volatility of the new portfolio if we invested 50% in A+B and the remaining 50% in C? You could potentially avoid computations.

Stocks	Volatility	% Portfolio invested	Average Return
A and B	27	50	15
C	32	50	18

1. Volatility will lie somewhere between 32% and 40%.
2. Volatility will lie somewhere between 27% and 32%.
3. Volatility will be below 27%.
4. Volatility will be above 40%.
5. Volatility will become zero.

Answer 1

• Volatility will lie somewhere between 32% and 40%.: If we combine a portfolio of high volatility with that of low volatility, then the volatility of the portfolio is bound to come down so the volatility of higher than 32% doesn't make sense so this option can be eliminated.
• Volatility will be above 40%.: If we combine a portfolio of high volatility with that of low volatility, then the volatility of the portfolio is bound to come down so the volatility of higher than 32% doesn't make sense so this option can be eliminated.
• Volatility will become zero: If we combine two assets of non zero volatility then there will be some volatility. If one asset is risk free then the entire volatility will be that of the non risk free asset. So volatility of the portfolio can only be 0 if the entire amount is invested in the risk free asset, so this option can be eliminated.

Now to see which of the remaining two option is correct, we need to solve the following equation:

• Volatility will lie somewhere between 27% and 32%. As the calculated volatility is lower than 27% this option is incorrect
• Volatility will be below 27%: .this option has been proven by above calculation so this option is correct. right option is option C