Re: How good is "Buy-and-Hold"? It is miserably bad.

[Bob Fulks <bfulks@xxxxxxxxxxxx>]

At 2:21 PM -0400 6/5/99, Mark Johnson wrote:

>How good is "buy and hold the S&P"?
>===================================
>
>Occasionally you'll see an article that dismisses
>a futures trading system because "it isn't much
>better than the performance of a simple buy and
>hold strategy".
>
>So, let's see what the performance of Buy and Hold
>actually is.

<snip>




Another way to make the comparison is by using the Sharpe Ratio which is,
in effect, a risk-adjusted return. An example might make this clearer.

Someone posted the code for a system called "Test0413" on another email
list. I tested it and have the numbers so I will use those numbers as the
example of a trading system (and not a very good one at that).

Buy/hold on back-adjusted S&P500 futures has averaged a 17.9% annual return
with a 13.8% annualized standard deviation of returns. This results in a
Sharpe Ratio of about 1.3:

     Sharpe = 17.9 / 13.8 = 1.3

(All of these calculations assume you are being paid interest on the margin
balance in your futures account but this is not a major factor in case you
are not.)

The Test0413 system measured an annualized return of 17.6% with an
annualized standard deviation of returns of 9.2% which is a Sharpe Ratio of
1.9:

     Sharpe = 17.6 / 9.2 = 1.91

So you can see that the return rate was a little lower than buy/hold but
the standard deviation was much lower. This is about what you would expect
since the system would have gotten us out of the corrections that we would
have experienced with buy/hold. But comparing the two based upon only the
returns would make buy/hold seem better.

But this is misleading.

To accurately compare, you would need to increase the leverage when using
Test0413 some to get its standard deviation up to the same as buy/hold. You
would need a leverage of about:

     Leverage = 13.8 / 9.2 = 1.50

To accomplish this you would buy three contracts using Test0413 for each
two contracts you would have bought for buy/hold.

Then, the Test0413 system with leverage would measure a return of 17.6% *
1.5 = 26.4% with a standard deviation of 9.2% * 1.5 = 13.8%

The Sharpe Ratio would remain at 1.90:

   Sharpe = 26.4 / 13.8 = 1.91

(Sharpe Ratio is not affected much by moderate use of leverage.)

So if you used leverage to adjust the risk when using the Test0413 system
to what it was with buy/hold, the return from using Test0413 would have
been 26.4% per year which is 1.47 times better than would have been
buy/hold.

This Test0413 system was not a very good system. It was just something
someone put together quickly as an example and posted the code publicly for
comments. Most good trading systems have a Sharpe Ratio of well over 2 and
values up to 3 or 4 are not uncommon. So a system with a Sharpe Ratio of 4
would be about three times better risk/return ratio than buy/hold over this
period. (And we all know that this period has been an exceptionally good
one for the market.)

Keep in mind that by using leverage you can increase the returns to any
amount you want. So comparing returns without considering the standard
deviation of returns is misleading.

Bob Fulks