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namssa
05-11-2008, 09:21 AM
There was a question where:
current portfolio return is 5%
target return is 5.25%

Then they gave you something like implied added return and volatility for each possible hedge fund. I think that the question asked which hedge funds would cause the portfolio to reach the required risk adjusted return.

Did anyone understand what they were getting at? If you can remember more details about the problem, that might be helpful too.

waha
05-11-2008, 10:01 AM
I used Sharpe ratio for comparison, end up with funds W and X having much better ratios whereas funds Y and Z having just moderately increased ratios.
So my recommendation is the go with either fund W or X. however, I made further comment that fund W has the same volatility as the current portfolio (believe is 10%) whereas fund X having higher volatility (20%) so even fund X's sharpe ratio is close to fund W, I recommend fund W is the best choice. I hope that I am not contradicting myself.

namssa
05-11-2008, 10:15 AM
I used Sharpe ratio for comparison, end up with funds W and X having much better ratios whereas funds Y and Z having just moderately increased ratios.
So my recommendation is the go with either fund W or X. however, I made further comment that fund W has the same volatility as the current portfolio (believe is 10%) whereas fund X having higher volatility (20%) so even fund X's sharpe ratio is close to fund W, I recommend fund W is the best choice. I hope that I am not contradicting myself.

So, you interpreted the top row of the table to represent mu - Rf? This is the part that I didn't get. I was thinking that the added return was over the existing portfolio, rather than the risk free return.

I think that makes sense. Then you could just calculate the risk adjusted target return as (5.25% - 5.00%)/10% and evaluate the hedge funds based on whether their Sharpe ratio exceeds this value.

waha
05-11-2008, 10:18 AM
namssa, sorry that I might have confused you, see I am still confused myself even two days after the exam :) What you said was exactly what I did.
(5.25-5.00)/10%, I remember in the exam, the extra return for each fund was given along with its volatility, right?

namssa
05-11-2008, 10:22 AM
namssa, sorry that I might have confused you, see I am still confused myself even two days after the exam :) What you said was exactly what I did.
(5.25-5.00)/10%, I remember in the exam, the extra return for each fund was given along with its volatility, right?

No problem. I understand now. I wrote on the exam that risk adjusted return should be based on the Sharpe ratio, but that I didn't understand how to interpret the given parameters. Now I understand how I should have interpreted it.

Thanks.

sundwarf
05-11-2008, 12:41 PM
I used Sharpe ratio for comparison, end up with funds W and X having much better ratios whereas funds Y and Z having just moderately increased ratios.
So my recommendation is the go with either fund W or X. however, I made further comment that fund W has the same volatility as the current portfolio (believe is 10%) whereas fund X having higher volatility (20%) so even fund X's sharpe ratio is close to fund W, I recommend fund W is the best choice. I hope that I am not contradicting myself.

Argh, i got to the same conclusion without doing any calculations... I just said both PEs added less return than fund W, but having higher volatility, and therefore they are eliminated automatically. At the same time, fund X has much higher volatility than the original portfolio, thus even though it has higher riskk-adjusted return than W (?), it's not as good a choice as fund W... I hope I won't get killed by writing this way...

Laurelinda
05-11-2008, 06:27 PM
Uh oh, did they ask us to recommend a particular choice? If so I missed that altogether! I thought they were just asking which, if any, of them met the target return on a risk-adjusted basis...I said they all did.

I used M-squared with the original portfolio substituting for the market.

iamsupertc
05-11-2008, 06:29 PM
Uh oh, did they ask us to recommend a particular choice? If so I missed that altogether! I thought they were just asking which, if any, of them met the target return on a risk-adjusted basis...I said they all did.

I used M-squared with the original portfolio substituting for the market.

that's what i wrote for this question too... although i just used Sharpe ratio

The Smokin' Cracktuary
05-12-2008, 08:49 AM
I also used sharpe ratios in some fashion, although I stated that you couldn't make a clear choice because you didn't know the correlations of the various options with the existing protfolio. Some of them may have had diversification benefits and could have actually reduced the overall portfiolio risk and added additional return.

Of course they didn't ask that, so I am sure it was not part of the solution. I am pretty sure that fell into the "I have three more minutes on this question and am out of stuff to write" area.

Caramel
05-12-2008, 02:29 PM
namssa, sorry that I might have confused you, see I am still confused myself even two days after the exam :) What you said was exactly what I did.
(5.25-5.00)/10%, I remember in the exam, the extra return for each fund was given along with its volatility, right?

I was confused by this question as well, and the following was my thoughts:

1) the portfolio risk premium is zero, with 10% vol. which implies Rp = Rf = 5%
2) the risk premium of each hedge fund is given and the target porfolio return is 5.25%
3) let Rp' = expected return of the entire portfolio including investment of hedge fund x, then

(Rp' - 5%)/vol. of hedge fund X = risk premium of hedge fund X

4) Solve Rp' and see if it's above or below the target portfolio return.
5) Select the hedge fund that will give the highest Rp'.

I got Hedge Fund Z with 5.45%.

Mr. BoH
05-12-2008, 03:51 PM
I used M^2, and assumed the risk-free rate was 4% (you have to have a risk-free rate to do M^2, yes?). My thought was that 5% can't be the risk-free rate since it has a volatility of 10% (and was described as 20% equity / 80% bonds, I think).

Doing this, I got that W and X (the 2 hedge funds) were better than current portfolio on a risk-adjusted basis, while Y and Z (the 2 private equity) were not.

No idea if this was the approach they were looking for, but it seemed reasonable.

The Smokin' Cracktuary
05-12-2008, 04:14 PM
I was confused by this question as well, and the following was my thoughts:

1) the portfolio risk premium is zero, with 10% vol. which implies Rp = Rf = 5%
2) the risk premium of each hedge fund is given and the target porfolio return is 5.25%
3) let Rp' = expected return of the entire portfolio including investment of hedge fund x, then

(Rp' - 5%)/vol. of hedge fund X = risk premium of hedge fund X

4) Solve Rp' and see if it's above or below the target portfolio return.
5) Select the hedge fund that will give the highest Rp'.

I got Hedge Fund Z with 5.45%.

I used M^2, and assumed the risk-free rate was 4% (you have to have a risk-free rate to do M^2, yes?). My thought was that 5% can't be the risk-free rate since it has a volatility of 10% (and was described as 20% equity / 80% bonds, I think).

Doing this, I got that W and X (the 2 hedge funds) were better than current portfolio on a risk-adjusted basis, while Y and Z (the 2 private equity) were not.

No idea if this was the approach they were looking for, but it seemed reasonable.

OK. So here is what I am reading. It seems as though people are applying some mix of the information ratio and the sharpe ratio. People are subtracting the return on the current portfolio in the numerator and then dividing by some volatility in the denominator. Which as far as I can tell makes no sense. Whether you divide by the portfolio volatility or the new asset volatlity, the statistic means nothing.

To use the information ratio you need the volatility of the asset minus the portfolio (tracking error volatility), which they don't give you. It makes no sense to use the new allocation's volatility in the denominator unless you use the risk-free rate in the numerator and not the portfolio return, which is the only thoeretically sound choice I can see (the sharpe ratio). But that doesn't really give you any information about which one to choose, unless you just maximize the sharpe ratio.

Maybe I am missing something? Am I misunderstanding the sharpe ratio or information ratio?

The Smokin' Cracktuary
05-12-2008, 04:15 PM
Also, using M^2 and sharpe will yield the same results. So I am sure if either one is the correct method, they both are.

sundwarf
05-12-2008, 04:31 PM
OK. So here is what I am reading. It seems as though people are applying some mix of the information ratio and the sharpe ratio. People are subtracting the return on the current portfolio in the numerator and then dividing by some volatility in the denominator. Which as far as I can tell makes no sense. Whether you divide by the portfolio volatility or the new asset volatlity, the statistic means nothing.

To use the information ratio you need the volatility of the asset minus the portfolio (tracking error volatility), which they don't give you. It makes no sense to use the new allocation's volatility in the denominator unless you use the risk-free rate in the numerator and not the portfolio return, which is the only thoeretically sound choice I can see (the sharpe ratio). But that doesn't really give you any information about which one to choose, unless you just maximize the sharpe ratio.

Maybe I am missing something? Am I misunderstanding the sharpe ratio or information ratio?

That's actually what I was thinking during the exam. We are not given risk free rate, nor that volatility we needed for information ratio, I was really reluctant to do any calculations. I used some kind of logic to explain things (see my earlier post), and got the a similar result as most other people. I don't care if I get most credit, as long as my answers are not dead wrong and my logic was okay I am satisfied.

Laurelinda
05-12-2008, 04:31 PM
Whether you divide by the portfolio volatility or the new asset volatlity, the statistic means nothing.

...

Maybe I am missing something? Am I misunderstanding the sharpe ratio or information ratio?

You might not be missing anything, it could have been me trying to come up with something and not making much sense.

Here was my reasoning:

We couldn't use the Information Ratio because it's the ratio of active return to active risk. As you say, we were given no measure for active risk because we didn't have any correlations. So I threw out that idea.

M^2 is a measure of the amount of return a portfolio would have received if it had the same amount of risk as the market. In this context it has the same bottom line as the Sharpe ratio.

Management had a certain amount of risk in its current portfolio and wondered if any of the alternative strategies would do better. They asked for a risk-adjusted analysis because they knew you couldn't just say, "Such-and-such is better than the current portfolio because it has an expected return 50 bps higher. Oh, wait, it also has twice the risk."

So to accomplish this risk-adjusted analysis, I thought, "What amount of return would these alternatives get if they had the same amount of risk as the current portfolio?" Hey! That sounded like a modified M^2, except we're comparing to the current portfolio instead of to the market.

So that's what I did, and I explained that it was "modified". Who knows whether that's what they wanted... :shrug: