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Bob, I think I disagree with your comments (below) and could I ask you to
help me better understand. I'm having difficulty with your example in which
you state that the doubling of exposure by the use of leverage also doubles
the standard deviation. Given the same performance of two portfolios with
differing SDs, how would a third portfolio identical to the first except for
the application of leverage to cause its SD to be equal to that of the
second portfolio prove your example?
Colin West
-----Original Message-----
From: Bob Fulks [mailto:bfulks@xxxxxxxxxxxx]
Sent: Thursday, March 29, 2001 11:22 AM
To: cwest@xxxxxxxxxxxx
Cc: omega-list@xxxxxxxxxx
Subject: RE: portfolio testing
At 10:16 AM -0700 3/29/01, cwest@xxxxxxxxxxxx wrote:
>Measuring on a risk-adjusted basis and it's inverse is a good measure
>of not only a portfolio, but the capability of a portfolio management
>application. Typically, I use the Sharpe ratio to measure a portfolio
>and then measure a leveraged benchmark, such as an index, so that it
>has the same Sharpe ratio as the portfolio, thus comparing ROI given
>normalized volatility and performance. Applying these kinds of
>measure really shows how poorly most fund managers, traders,
>analysts, and so on actually do. Very few analysts can even show me
>an audited track record, yet they ask thousands for their services
>:). BTW, I won't mention the stellar performance of mutual funds when
>so scrutinized.
The Sharpe Ratio of the index does not change with changes in leverage.
Sharpe = (Return - Risk_free_return) / Standard_deviation
Using an example:
Sharpe = (25% - 5%) / 20% = 1.0
If you double the exposure with 100% leverage, the Return doubles to
50% and the Standard_deviation doubles to 40%. But you have to reduce
the Return by the interest you pay on the leverage used (assume 5%)
so the Return becomes 50% - 5% = 45%. Then:
Sharpe = (45% - 5%) / 40% = 1.0
What I suspect you mean is that you change the leverage on the index
until the volatility of the leveraged index equals the volatility of
your trading results and then compare the ROI of the two. This is a
correct approach. This is what some people call the "risk-adjusted
return". (Usually they adjust the volatility of the portfolio to
match that of the index but it is the same idea.)
But you can get the same valid comparison by just comparing the Sharp
Ratio of the two directly.
>I've been searching for a portfolio manager for some time, but still
>to no avail. Except for a few, can the world be in denial of real
>performance measurement.
They don't want you to understand this since if you did, you would
take your money elsewhere. Most of them do poorer than the index. All
big brokerage companies track the Sharpe Ratios of the money managers
they use for their wrap accounts but will normally not disclose this
to the customers.
The Hulbert Financial Digest compares the performance of investment
newsletters using a risk-adjusted return and very few beat an index
fund.
The MoniResearch Newsletter ranks the performance of market-timer
money managers using an Ulcer Index which is similar. Some of these
do much better than the indices but the best programs are usually
maxed out and closed to new investors.
Last September, I went to the MorningStar website and did a search
for mutual funds with a Sharpe Ratio of greater than a given value.
The result was that only about 10% of the funds did better than an
index fund and 44% of all funds did poorer than investing in T-Bills.
(Details below.)
Bob Fulks
---------
Sharpe Ratio No. of Funds
>= + 3.0 1 (A short-term Bond Fund with 6.9% return)
>= + 2.5 3
>= + 2.0 5
>= + 1.9 5
>= + 1.8 5
>= + 1.7 6
>= + 1.6 8
>= + 1.5 10 (Most of these are Bond Funds)
>= + 1.4 16
>= + 1.3 36
>= + 1.2 81
>= + 1.1 169
>= + 1.0 375
>= + 0.9 744
>= + 0.87 873 (The Vanguard 500 Index fund value)
>= + 0.8 1212
>= + 0.0 4786 (Funds below this level made less than
T_Bills)
>= - 1.0 8298
>= - 2.0 8501
>= -10.0 8538 (I assume Sharpe Ratio is not available
for all others)
All Funds 11963
So out of probably 8538 funds for which Sharpe Ratio data is calculated:
> About 4% of all funds had a Sharpe Ratio >= 1.0
> About 10% of all funds had a Sharpe Ratio >= the largest S&P Index
fund.
> About 44% of all funds made a lower return than T-Bills
Bob Fulks
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