ok, I was too hasty, but I can tell you there must be something wrong. How could the Std dev of teh overall portfolio be less than 6%, when the active std dev = 15.6% and the passive port = 20%? If so, you have reduced risk way too much, with a return of 10% given, the market return must have been much higher.
there is a passive portfolio which is THE MARKET PORTFOLIO
there is a Active portfolio which is a portfolio constructed with positive alpha stocks.
the optimal portfolio is a combinaison of those 2 ptf. so there is no 0 std dev
and the active porfolio does not have 15.6 sigma since you have no information about the return ( the 10% is the return of the OPTIMAL portfolio ) so you cannot calculate the stdev of active portfolio since you dont have his return.
i whish i can look at the real question to figure it out since im confident that there is something wrong here,
The 0.45 sharpe ratio in the question is for the optimal risky portfolio. So you plug everything into the Sharpe ratio, solve for the std dev, then multiply by 0.3 seeing as the rest of the portfolio is in a risk free asset.
Sorry my bad. I overlook the problem. Actually I can’t copy paste it here. ( I misunderstand the Treynor black model Sorry again for making you spending much time here.
Kiakara: do you understand the answer? Can you pls explain for me?
The optimal risky portfolio determined by Treynor Black has an allocation of 30% to the active port and a sharpe ratio of 0.45. Given that the risk free rate of 3%, the std dev of market (passive) port is 20%. The expected return on the optimal risky portfolio is 10%, the std dev of an investor’s optimal risky port that is allocated 70% to risk free asset is closest to :