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# Yet another Treynor Black Model question

LondonPosts: 749 Sr Portfolio Manager
The question is as follows:

You are using the Treynor-Black Model for security selection. The optimal portfolio consists 40% of actively managed portfolio with an expected return of 10%. The rest is allocated to the indexed portfolio, which has an expected return of 6%. Your client's requirements are for a portfolio that has an expected return of 10%. Which of the following is the ideal way to achieve this?

A Allocate 100% of the client's funds to the active portfolio
B Allocate 100% of client's funds to the indexed portfolio and borrow money to leverage
C Keep the optimal portfolio allocation the same and leverage the optimal portfolio by borrowing.

Based on my understanding, if 40/60 is the optimum portfolio which would only produce an expected return of 7.6%, you have to alter the weightings towards the actively managed portfolio, but the point is if 40/60 is the optimum how would I be able to adjust it?

• C? I assume short positions are possible?
• LondonPosts: 749 Sr Portfolio Manager
edited April 2013
@reena yup the right answer is C, but what does 'leverage the optimal portfolio by borrowing' means?

From my understanding, that means to invest the funds from shorting the 60% indexed portfolio to the actively managed portfolio?

How would you be able to benefit from diversifying in the indexed portfolio?
• Posts: 2,010 Sr Partner
Sorry @vincentt, I couldn't resist this... )

• Posts: 2,010 Sr Partner
@vincentt - I'd think leverage here means borrowing money to fund the optimal portfolio, which would amplify it's returns.

Compare a case where an investor borrowed 50% of the money to fund an initial \$100 optimal portfolio. And say the optimal portfolio appreciated by 10%.

Unleveraged return = (\$110-\$100) / \$100 x 100 = 10%
Leveraged return = (\$110-\$100) / \$50 x 100= 20%

His leveraged return doubled when he borrowed 50%. Of course the opposite is true if the price fell. Note that this simple example has not adjusted for the cost of borrowing that money, which would slightly reduce the leveraged return %.
• LondonPosts: 749 Sr Portfolio Manager
@sophie lol

I understand the leverage return, but wouldn't that unbalance the optimum portfolio? Since by borrowing more to invest in the actively managed portfolio, you are actually altering the optimum weighting and towards the actively managed.

• Posts: 2,010 Sr Partner
Hmm... I would have thought the optimum portfolio remains the same. You are not changing the composition % of it by borrowing the money. you are just amplifying potential return (upsides and downsides) of it by borrowing money.
• LondonPosts: 749 Sr Portfolio Manager
edited April 2013
ahhh!!! that's true! I keep having the mindset of the SML model or the ones from level 1.

if investor wants higher return or riskier portfolio, move up the line (towards the right) so you'll get less risk-free portfolio and more riskier portfolio hence higher return.

thanks @sophie
• Posts: 20 Associate
@sophie is right, the portfolio would still remain the same balance of 40/60 but the larger value of investment would mean the 7.6% return on the 150% of the initial value would be closer to 10% of the original value of the investment.

• Posts: 2,010 Sr Partner
No problem @vincentt!

Thanks @Gary, and welcome to the forum! Are you taking Level 1 June then?
• Posts: 20 Associate
edited April 2013
Thanks @Sophie I am sitting the Level 1 in December thought i'd start early. Some of it is familiar but i don't want to get too complacent .

Ps Love that Animated Gif i may have to borrow for work