Should be like a levered bond portfolio.
(Tangent return - D * Rfr)/E
A simpler way is derive the sharpe ratio, and use that to solve for the standard deviation of the levered portfolio, the ratio of the new sd/old sd is your leverage.
You will get a different answer if you use the ratio of standard deviations vs using the previously mentioned formulas where you calculate leverage based off of expected return. The weighted standard deviations using simple arithmetic weightin will over state risk therefore you will get a different answer using arithmetic SD ratios.
Correct me if i’m wrong.
I’ll get back to it when I get home, currently on phone.
Are you all just asking how you would solve for the e® when including the RFR? It’s the same as you would when choosing any other corner portfolio. There is no difference.
You mean w and 1-w?
I did something simillar in the exam, then divide them to get leverage.
Guys it’s the exact same formula for 2 corner portfolios but Rf instead the corner portfolio. That’s it. The formula of (levered return = unlevered return + [D/E * (unlevered return - cost)] is exactly the same formula of w and 1-w !!!
Suppose P = 7.5, Rfr = 2 E® = 10
Then w(rfr) = -0.45 w§ = 1.45
So 0.45/1.45 = 31% borrowed.
That’s how I’d do it.
This hypothetical question was asking for weights though wasn’t it? so .45 and 1.45 would be right…
If portfolio 7.5%, E® = 10% Rfr = 2%, SD§ = 20%
Then Sharpe = 0.275
10 = 2 + 0.275x
x = 29%
29/20 = 1.45
Leverage = (1.45-1)/1.45 = 31%
How much do you need to borrow, or D/E.
I don’t think writing down one more step would deduct points if you got this far, hope not at least.
Correction, the leverage I used is D/A.
45% would be D/E
Where are you getting the Standard deviation of the portfolio from? Your method works if you are given standard deviation or the Sharpe of the final portfolio - otherwise you don’t know what the Sharpe is and cannot solve for SD of the portfolio.
Essentially adding a risk free asset reduces the standard deviation of the final portfolio so the method you are using does not work without having the SD of the final portfolio provided.
Hmm never mind - it looks like you get the same answer using your method or the other method.
Anyone has a different view?
Just draw the efficient frontier to see which portfolio gives the minimal sd given specifc return. leverage port. vs. corner pf
No, you borrowed 45%, your leverage denominator is incorrect. You divide by equity not total assets.
No, you borrowed 45%, your leverage denominator is incorrect. You divide by equity not total assets.
yes you would borrow 45% because if you net both weights you`ll get a 100%. weights must sum up to a 100%
…
Too low, that would add like 0.1%