Problem in Treynor black

Anyone please help me with this problem:

Optimal risky port. determined from Treynor model has 30% in active port. and 70% in passive port.

Sharpe ratio of active port = 0.45


Std dev of passive port = 20%

E® of optimal = 10%.

What is std dev of this optimal portfolio??


you are missing something somewhere,

without covariance you cannot do this problem, there’s is probably a sentence saying, both portfolio are not correlated or something

It looks like it is straightforward unless I’m way off!

Rp-Rf/Sp = 0.45, that’s the given Sharpe Ratio.

Plug and you should get 15.6%.

now you have the std dev of the Active portfolio,

not the optimal portfolio.

@Summerside: Nothing is missed. That’s all of the problem

@Dreary: three possible answers are

  1. 4.7%

  2. 5.2%

  3. 6%

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.

where this question come from max?

Swchzer practice test 1

70% of portfolio is in risk free asset (std dev is zero). std.deviation of activeportfolio is 15.6. so, 0.3 x 15.5=5.2%

allright can’t find it you are not helping much so i give up a question number a page would have been helpfull for not losing my time

there is no risk free asset here,

in treynor black :

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,

no no no.

The question says:

Optimal risky port. determined from Treynor model has 30% in active port. and 70% in a risk-free asset.

so as i said, he was wrong.

then if it’s risk free asset the problem is different. i lost 15 minutes of my life because of this

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.

I did this q yesterday. Got it wrong :frowning:

max made the worst copy paste of a question I ever saw.He even double checked it and felt like his copy paste was 100% good.

next time just take the time to copy paste it the good way so we all save time.

yes that’s bad…it’s already hard as is.

Sorry my bad. I overlook the problem. Actually I can’t copy paste it here. ( I misunderstand the Treynor black model :frowning: Sorry again for making you spending much time here.

Kiakara: do you understand the answer? Can you pls explain for me?

So here is the full problem:

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 :




10 -3 / 0.45 = 15.56

0.3X + 0.7(20) = 15.56

x = (15.56 - 14 ) / 0.3 = 5.2

Nah the answer is A