Bill Benter's Sharpe Ratio?

[prank]

Does anyone have a reference on Bill Benter's Sharpe Ratio?

For that matter, can anyone cite the SR for many (or any) leading handicappers?

Thanks!

Prank

[robert99]

Prank,

I have never heard of any "handicapper" calculating that figure. Those who follow systems and staking plans sometimes calculate it to compare one system against another, over the longer term - but systems players are not usually professional "handicappers".

You are not really choosing between different asset risk types for longer term "investment" purposes. You are usually controlling risk by better estimating the true price than other bettors at the time and only betting when that price is in your favour - which is essentially what Benter etc did. It is not the bet "asset" that it is the risk - it is the rightness or wrongness of the competing market view a few minutes before the race result.

"The William F Sharpe ratio quantifies how effectively a portfolio of bets utilises risk to maximise return. It is defined as the effective return per unit of risk. The expected portfolio of bets return is predicted from historic data, and the standard deviation of the asset mix is traditionally used as a proxy for risk (or volatility). A higher Sharpe Ratio essentially signifies a more risk efficient portfolio. It calculates the optimum mix for a portfolio or single betting strategy by maximising its Sharpe ratio."

[prank]

You are not really choosing between different asset risk types for longer term "investment" purposes. You are usually controlling risk by better estimating the true price than other bettors at the time and only betting when that price is in your favour - which is essentially what Benter etc did. It is not the bet "asset" that it is the risk - it is the rightness or wrongness of the competing market view a few minutes before the race result.


Thanks for the response! I realize that although handicapping means predicting a probability distribution, and so on its face it doesn't look the same as other markets, there's still a mean and variance that can be calculated, and I think that that can yield a Sharpe Ratio. For a gambling "syndicate", this may be meaningful in comparison to putting their money in an index fund. :)

Another point that you mention is important - the estimation of the probabilities (handicapping ;-)) is certainly important, but it's only part of the problem. Choosing how much to wager is the other concern. High payoffs for high risk are important, but being able to take advantage of low risk situations is also important, though these are probably very rare. :)

What I think may be hard to overlook is that a handicapper could inflate their Sharpe Ratio by finding very rare, "sure bets". So, the level of the participation in making many wagers is another important consideration. Benter mentioned in his '94 article that they only passed on about 5% of the races, which seems pretty impressive.

Anyway, I'm just curious. I think the SR is kind of a poor measure, but friends in finance seem to think it's special, so I wanted to get a sense of what a good handicapper could achieve.

Thanks!

PRank

[Sinner369]

You mentioned the Benter article from "94"..............Is there a link to this
article?

I'd like to read the whole article!


sinner:p

[Premier Turf Club]

http://en.wikipedia.org/wiki/Sharpe_ratio

I used this in my Monte Carlo simulation model. For example

Lets say two horses had a mean sheets # of 9, but had these distributions;

A: 7 or less 5%, 7-8, 10%, 8-9 30%, 9-10% 45%, 10-11, 10% 11+ 5%

B:A: 6 or less 10%, 6-7, 15%, 7-8 10%, 8-9% 15%, 9-10 15%, 10-11 15%,11+ 20%

If they were both the same odds, horse A would have a higher sharpe ratio than horse B, less volatility for a given average figure.

These examples come up all the time in handicapping, a need to lead time that runs monster figures when he clear, but folds when looked in the eye, low mean (on a Sheets scale) higher standard deviation. What I found in years of research is that high Sharpe ratio horses, even with lower (worse) mean figures are very good bets to hit the baord and make good exotic keys.

[prank]

You mentioned the Benter article from "94"..............Is there a link to this
article?

I'd like to read the whole article!


Sorry, I don't know of an electronic copy. It's in "Efficiency of Racetrack Betting Markets", by Hausch, Lo, and Ziemba.

[robert99]

http://en.wikipedia.org/wiki/Sharpe_ratio

I used this in my Monte Carlo simulation model. For example

Lets say two horses had a mean sheets # of 9, but had these distributions;

A: 7 or less 5%, 7-8, 10%, 8-9 30%, 9-10% 45%, 10-11, 10% 11+ 5%

B:A: 6 or less 10%, 6-7, 15%, 7-8 10%, 8-9% 15%, 9-10 15%, 10-11 15%,11+ 20%

If they were both the same odds, horse A would have a higher sharpe ratio than horse B, less volatility for a given average figure.

These examples come up all the time in handicapping, a need to lead time that runs monster figures when he clear, but folds when looked in the eye, low mean (on a Sheets scale) higher standard deviation. What I found in years of research is that high Sharpe ratio horses, even with lower (worse) mean figures are very good bets to hit the baord and make good exotic keys.


Premier TC

The volatility aspect was discussed in "Measuring Volatility in a Horse's Performance" thread. I quite agree with with you, but it was uphill in persuading anyone else of this important technique and philosophy.

http://www.paceadvantage.com/forum/showthread.php?t=35740&highlight=volatility

[prank]

Thanks for the link on the discussion of horse variability. I'll post over there on that topic, and welcome any insights on handicapper performance and risk measurements. :)

Prank

[Robert Fischer]

interesting thread here...

[highnote]

William T. Ziemba, Ph.D (Dr. Z in the horse racing world) writes in the abstract to "The Symmetric Downside-Risk Sharpe Ratio and the Evaluation of Great Investors and Speculators":

The Sharpe ratio is a very useful measure of investment performance. However, it is based on mean-variance theory and thus is basically valid only for quadratic preferences or normal distributions. Hence skewed investment returns can lead to misleading conclusions. This is especially true for superior investors such as Warren Buffett and others with a large number of high returns. Many of these superior investors use capital growth wagering ideas to implement their strategies which leads to higher growth rates but also higher variability of wealth. A simple modification of the Sharpe ratio to assume that the upside deviation is identical to the downside risk provides a useful modification that gives more realistic results.

The full paper can be downloaded from this link:

http://www.gloriamundi.org/ShowTracking.asp?ResourceID=453058181

He talks about Benter on page 10.

[prank]

Thank you very much! This paper looks like it'll be very enjoyable reading!

I agree that the Sharpe Ratio doesn't provide a terrific measure of success, but it's like IQ or GPA - it's a little diagnostic that often useful in discriminating between the high performers and the median, though not always - some people excell in ways that a Sharpe Ratio (or IQ or GPA) doesn't account for. It's interesting to see how it might be modified to be more informative for some approaches to risk.

[Foolish Pleasure]

Can you spend Sharpe ratio at the local supermarket?

Then who cares?


Obviously your friends in finance are more concerned with shilling some picks service vs actually making money.

perfect for a board loaded with authors, shills and touts.

[highnote]

Thank you very much! This paper looks like it'll be very enjoyable reading!

My pleasure. I hope you find it useful.

The thing I found most interesting about the Sharpe ratio is that if an investor is incredibly successful and makes a lot of money the Sharpe ratio does not give as good of a grade as you'd expect. That is because the Sharpe ratio penalizes high returns with volitile records. So the modified Sharpe ratio gives a more realistic measure of the successful investor.

Ziemba gives a lecture on the great investors. Interestingly, Benter is on the list, along with Buffett and Thorp. All three turned modest starting bankrolls into large fortunes. And all three are Kelly bettors.

The fact that they are all three Kelly bettors is important. When you are investing over time it is capital growth theory (Kelly criterion) that gives the most long term growth. The utility function behind the Sharpe ratio is quadratic.

Kelly bettors will have more volatility, but end up with more money than other investors. However, Thorp has only had 3 losing months in the past 300 or so months, so there are exceptions.

I especially like Figures 4 and 5 on pages 10 and 11 where Ziemba provides charts to show the difference between gamblers and other investors. He has a good sense of humor. The so-called gamblers are Benter and Thorp. :D


He writes:

The gamblers had several common characteristics:

• they carefully developed anomaly systems with positive means;
• they carefully developed computerized betting systems that automated the betting process;
• they constantly were updating their research, and
• they were more focussed on not losing than winning in their carefully done risk control.

[Foolish Pleasure]

All three turned modest starting bankrolls into large fortunes. And all three are Kelly bettors.

The fact that they are all three Kelly bettors is important. When you are investing over time it is capital growth theory (Kelly criterion) that gives the most long term growth. The utility function behind the Sharpe ratio is quadratic.

Kelly bettors will have more volatility, but end up with more money than other investors









Sorry not even close to reality here folks.


The one thing your gamblers all had in common was exactly the bread and butter of successful gambling-A HUGE INFORMATION EDGE-their money management had nothing to do with their success and in fact obviously hindered it.

how much more money would all three of your idols have if they had bet two times Kelly?


Ultimately that is why this is not reality,
who on your list or anywhere for that matter who has made it good using KELLY would not have made it alot better being more aggressive? Thorp? His backers had just abt given up-another tap out may have been the end? I doubt it, his informational edge due to the counting would have found a ready made line of new money.



The KELLY CRITERION has an implicit assumption of a static enviroment.


WHo made out better people betting KELLY at Pinny or people overbetting it because they knew that eventually the FED would make it tougher to bet at PINNY?





Three guys ROTFLMAO-

go google Stevie Cohen, guy has paid himself a billion dollars the last 5 yrs, John Tudor Jones-guy could not tell you Kelly fr a toilet,
find an edge bet as much as you can at the price,because that edge is diminishing everyday,
and the present value of money and the ability to replace the BR trump the security of 1 and 2% bets.



Optimally solving the problem requires a little more imagination than doing a little junior high algebra,




there is comfort in a nice neat system or plan that completely divorces the brain fr the problem. Most people should not only bet more money, but bet alot more money-either shit or get the off the pot-likelihood of being talented enough to win but being such an idiot as to overbet yourself into the poor house are so slim-I know exactly ONE GUY that has done that and of course what is the next step for guy with talent who taps out due to overbetting????


easily replaced bankroll because he has talent means he is back in the game in no time and merely needs to choke down the enthusiasm at the windows.

[highnote]

Sorry not even close to reality here folks.

Do you deny these men made significant fortunes beginning with small bankrolls using the kelly criterion to optimally calculate the size of their wagers given their edge and their betting wealth and by allowing themselves a long enough time horizon?



The one thing your gamblers all had in common was exactly the bread and butter of successful gambling-A HUGE INFORMATION EDGE-their money management had nothing to do with their success and in fact obviously hindered it.


Yep. Buffett could sure use a better money management plan. As you said, the second richest man in the world is obviously hindered by it.

Maybe you can get a job consulting for him and show him how to become the world's richest man. ;) Just kidding.



how much more money would all three of your idols have if they had bet two times Kelly?

Dunno. How much?

One could argue that it is impossible to know unless you could see the record of all their bets.

It is doubtful that Thorp or Buffett are full kelly bettors.

In Buffett's case it would be irresponsible to shareholders to bet all of his $120 billion on one investment. Better to find lots of small $1 billion investments with a big edge. Plus, who I am to tell Buffett how to bet? He's done quite well without me.

I read somewhere that Benter reached a $100,000 win bet limit due to pool size limitations. Larger bets would have diminished his edge. So betting twice Kelly would have affected his odds. Which is OK when you win. But why risk losing twice as much at lower odds? That seems like a recipe for wealth erosion.


Ultimately that is why this is not reality,

Really?

who on your list or anywhere for that matter who has made it good using KELLY would not have made it alot better being more aggressive?

Dunno. Who?



WHo made out better people betting KELLY at Pinny or people overbetting it because they knew that eventually the FED would make it tougher to bet at PINNY?

Does Kelly apply here? Isn't the purpose of the Kelly criterion maximizing the long run growth of wealth. Knowing that the Fed would make it tougher to bet at Pinny means that the time period is unknown and probably short. Still, is that a good enough reason to overbet?

A Buffett investment might take years to turn a profit. Plus, is a Buffett/Thorp-like investor even going to consider pursuing investments that require an offshore bookmaker? Wouldn't they stick to more traditional forms of investing like the stock market?





Three guys ROTFLMAO-

go google Stevie Cohen, guy has paid himself a billion dollars the last 5 yrs,

Cohen reportedly paid himself $1 billion in 2005. It looks like his company, SAC, has quite a set of diverse holdings. He's hardly putting all his eggs in one basket by making one or two big bets on one or two events. Looks more like a Buffett-type investor to me. Of course, this could be wrong. This info was gotten from Wikipedia.

Jim Simons, Kelly bettor, of Renaissance paid himself a billion last year.


John Tudor Jones-guy could not tell you Kelly fr a toilet,

Don't know him.





find an edge bet as much as you can at the price,because that edge is diminishing everyday,


This probably depends on the investment. Some investments probably have edges that are growing every day.



and the present value of money and the ability to replace the BR trump the security of 1 and 2% bets.



The optimal strategy probably depends on the rules of the game and the situation in which one finds himself.


Optimally solving the problem requires a little more imagination than doing a little junior high algebra,

No doubt.




easily replaced bankroll because he has talent means he is back in the game in no time and merely needs to choke down the enthusiasm at the windows.

If his bankroll is easily replaced then he probably has not overbet.

Bottom line. There is more than one way to skin a cat. If Kelly doesn't work for you, then don't use it. It isn't for everyone. It's obviously served the three "gamblers" very well. Long Term Capital hedge fund didn't use it and we know what happened to them.

One thing is certain, overbetting and losing is more harmful to the bankroll than underbetting and losing.

Or as Dr. Z wrote, "Bet only when you have an edge. And never overbet."

[robert99]

Sorry not even close to reality here folks.

The one thing your gamblers all had in common was exactly the bread and butter of successful gambling-A HUGE INFORMATION EDGE-their money management had nothing to do with their success and in fact obviously hindered it.

how much more money would all three of your idols have if they had bet two times Kelly?

Ultimately that is why this is not reality,
who on your list or anywhere for that matter who has made it good using KELLY would not have made it alot better being more aggressive? Thorp? His backers had just abt given up-another tap out may have been the end? I doubt it, his informational edge due to the counting would have found a ready made line of new money.

The KELLY CRITERION has an implicit assumption of a static enviroment.

Optimally solving the problem requires a little more imagination than doing a little junior high algebra,


FP,

The object of even considering the Sharpe Ratio is when trying to see whether one betting strategy reaches the same or higher profit level but with less risk than another strategy. It is not actually about profit level. It is about optimum choice of a sustainable money management/ investment strategy that gives you the best chance. A profitable edge is a different topic. If you have not got one, then Sharpe type analysis just allows you to go bankrupt more slowly - that is all. If you do have one, then you get richer with less risk, so can afford higher stakes provided the market can sustain them (which it often can't).

If you bet less than 1.0 Kelly you make less than an optimum profit. If you bet 2.0 times Kelly, then by definition of an optimum you make sub-optimal or less profit, or, more likely, go bankrupt very quickly. Unless the odds are hugely in your favour or your "huge information" edge is applied correctly then without a sustainable money management strategy you also go bankrupt in the long term. Many good handicappers without money management skills eventually end up amongst the 96% who lose.

Kelly theory can be applied equally to varying levels of overlay over the bettor's estimate of true odds - it is not static. It is the latter estimation which is the difficulty to estimate in a single race but not over the long term. If you get your true odds wrong race by race even if on "average" they are right then you will also likely go bankrupt using a Kelly that is based on wrong edge data. There is a risk here that can be identified and managed better by such topics as Sharpe Ratio. I doubt if anyone learnt how to do any of that in any junior high school.

[formula_2002]

This may be a good place to ask some questions about Benter's "Computer Based Horse Race Handicapping And Wagering System" paper.

Lets start with this:
Table 3 ROI (act/exp) sums to 1.19
Table 4 ROI (act/exp) sums to .87

The combined (tables 3 and 4) roi 1.05

That means a proportion odds bet on ever horse in table 3 and 4 returns a positive roi.

Note: In the same manner, table 1 also returns a positive roi of 1.06
That means,if there were no trake take-out, a proportional odds bet (dutching) would return a 6% profit.

Would you say that is correct?

[arkansasman]

Formula,

Is Table 3 titled, Fundamental Model vs Actual Frequency when public estimate is greater than Model estimate, or am I looking at the wrong paper?

John

[formula_2002]

Formula,

Is Table 3 titled, Fundamental Model vs Actual Frequency when public estimate is greater than Model estimate, or am I looking at the wrong paper?

John
Yep, thats the paper

[arkansasman]

Formula,

I don't think that table has anything to do with ROI, unless I have missed something.

John

[formula_2002]

Formula,

I don't think that table has anything to do with ROI, unless I have missed something.

John

actual winners / expected winners = roi
If you bet 10, 3-1 shots, each with a 25% chance of winning, and you won 4 of 10 races , you were only expected to win 2.5 races.
4/2.5 = 1.60 roi.
you got back $32 and you bet $20. 32/20 =1.60.
If there was a 15% take your roi decreases to 27.2/20 = 1.36

[jfdinneen]

David Edelman, Quantitative Finance lecturer, handicapper, and author derives a sportstrading version of the Sharpe Ratio on page 28 of "The Compleat Horseplayer".

SR = (ProbWin - (1 / DecimalOdds)) / Sqrt(ProbWin * (1 - ProbWin))

For example, with the following 'investments', A is judged to be slightly better than B in terms of expected return per unit of risk:

A: ProbWin = 45%, DecimalOdds = 2.60

SR = (0.45 - (1 / 2.6)) / Sqrt(0.45 * (1 - 0.45))
= 0.13142

B: ProbWin = 31%, DecimalOdds = 4.00

SR = (0.31 - (1 / 4.0)) / Sqrt(0.31 * (1 - 0.31))
= 0.12973

John

[formula_2002]

David Edelman, Quantitative Finance lecturer, handicapper, and author derives a sportstrading version of the Sharpe Ratio on page 28 of "The Compleat Horseplayer".

SR = (ProbWin - (1 / DecimalOdds)) / Sqrt(ProbWin * (1 - ProbWin))

For example, with the following 'investments', A is judged to be slightly better than B in terms of expected return per unit of risk:

A: ProbWin = 45%, DecimalOdds = 2.60

SR = (0.45 - (1 / 2.6)) / Sqrt(0.45 * (1 - 0.45))
= 0.13142

B: ProbWin = 31%, DecimalOdds = 4.00

SR = (0.31 - (1 / 4.0)) / Sqrt(0.31 * (1 - 0.31))
= 0.12973

John

Some day, when I have an edge, I'm really going to look into this :rolleyes:

[GameTheory]

actual winners / expected winners = roiNo. Expected winners is the number of predicted winners by the model, not the odds. The odds have nothing to do with that table. That's why it is called "Fundamental Model vs Actual Frequency" and not "Public Odds vs Actual Frequency".

[alysheba88]

One thing is certain, overbetting and losing is more harmful to the bankroll than underbetting and losing.

Or as Dr. Z wrote, "Bet only when you have an edge. And never overbet."

I think the main point here was about underbetting and winning.

If you are losing does not matter. Slow death or quick death, you are still dying

[alysheba88]

As an aside do people really care about ROI? I mean seriously- not being a wise ass. Do players really focus on that?

[Dave Schwartz]

As an aside do people really care about ROI? I mean seriously- not being a wise ass. Do players really focus on that?

I do.

[formula_2002]

No. Expected winners is the number of predicted winners by the model, not the odds. The odds have nothing to do with that table. That's why it is called "Fundamental Model vs Actual Frequency" and not "Public Odds vs Actual Frequency".

Thanks.
It would help me if he did have a table ,"Public Odds vs Actual Frequency".
For me, it's all about ROI..

[GameTheory]

Thanks.
It would help me if he did have a table ,"Public Odds vs Actual Frequency".Don't you? Don't you have posters and wallpaper and tablecloths all over your house with such tables? That's how I imagine your house to be...

[formula_2002]

Don't you? Don't you have posters and wallpaper and tablecloths all over your house with such tables? That's how I imagine your house to be...

:sleeping:

[arkansasman]

It would help me if he did have a table ,"Public Odds vs Actual Frequency".

He does.

[formula_2002]

He does.
Well, there are only 12 tables, which one is it?

[formula_2002]

Table 8 (example race)

can someone tell me the tote board odds?

the table's public probabiliy estimate is, according to the table, (1-take)/div.

the div is the expected return/combined probability estimate

the combined probability exstimate (according to formula 1) includes the public's probability estimate.

catch 22(?)

[arkansasman]

can someone tell me the tote board odds?

The Dividend - 1 would be the odds

Dividend = 1-take/public probability (approximately - you have to round down for breakage)


John

[formula_2002]

The Dividend - 1 would be the odds

Dividend = 1-take/public probability (approximately - you have to round down for breakage)


John
Thanks.
Then 1/(odds+1) sums to 1.21,
1-(1/1.21) = 17.4% take out.
(I'll note that The combined probabilities sum to 1 and the
public's probabilities sum to 1)
-----------------------
Then if his combined probabilities are 100% correct and he gets the track odds (from which combined probabilities are calculated) then his "er", which is what I call ROI, ( actual winners/expected winners will) are one and the same.

All is well in the world..thanks again.