[PeterWellington]

I occassionally find arbitrage opportunities on money lines. It's easy to calculate a return on investment in these cases because there is a certain outcome.

For example:
Team A: -120
Team B: +130

Bet $100 on Team A and $79.71 on Team B. No matter which team wins, there's a profit of $3.62.

Return on investment = 3.62 / (100 + 79.71) = 2%

However, I've also created a system that lets me know if I have a statistically exploitable pair of spread bets.

For example (NBA game):
Team A: -105 +4
Team B: -105 -3

Based on historical data, the odds of a push on 3 and 4 are 3.9% and 3.5% respectively. So, there's a 7.4% chance of a push and a (1 - .074) chance of no push. On a $105 bet on both sides, I win $100 7.4% of the time and lose $5 92.6% of the time.

Expected value = (100 * .074) + (-5 * .926) = $2.77
Expected return on investment = 2.77 / (105 + 105) = 1.3%

Here's the problem. Due to my resources not being unlimited, there are times where I have to decide between different opportunities. For example, do I invest in a sure thing with a return of 1% or in a statistically profitable opportunity that returns 2% (knowing that I'll lose money more often than not)? Ideally, I could use some type of formula to calculate a risk adjusted return. I've looked at the different measures in the stock market but haven't found anything that translates well.

Any ideas are appreciated.

[Willie Bee]

Sounds like a question for our mod Ganchrow. But welcome to SBR

[gerry]

IMO, it's not a purely statistical thing. There are emotions involved. People generally feel rather happy by consistantly winning a little while frustrated by consistantly losing but occasionaly winning a lot. In other words, small variance or low risk is preferred by human nature. Your emotional fluctuation is not free - it worth money!
If you enjoy gambling or can stand the frustration in case of losing, just do whatever is statistically more profitible. It depends on the person.
BTW, past performance is not guarantee for futher prediction, especially because you don't know the underlying model. The statistics are bogus.

[RickySteve]

Originally Posted by PeterWellington

Ideally, I could use some type of formula to calculate a risk adjusted return. I've looked at the different measures in the stock market but haven't found anything that translates well.

You haven't looked very hard.

[bigboydan]

Let me welcome you to the SBR forum

I'm not much of an ARB type player myself. However, I feel Ganchrow would better answer this question from a stat point of view.

[Jay Edgar]

PeterW, BTW, that was a "Welcome to the Forum" from RickySteve as well.

A mild one, believeyoume.

[PeterWellington]

gerry, thank you for your thoughts. I agree with a lot of what you say. I do think there's a real price (aside from any emotions) you pay when you take on more risk (without an infinite number of "trials", or bets in this case). This is why a government bond might give you a return of 5% (essentially a sure thing) but you'd never think of investing in most stocks at that expected rate (added risk).

Ricky, I've looked at several options and have found some things that come close. I guess I'm having trouble fitting certain market measures into a betting model. For example, beta really has nothing to do with what I'm talking about but is present in many formulas I've come across. Also, I think something like standard deviation isn't directly applicable because the possible returns look nothing like a standard bell curve. I'd appreciate any suggestions you have or resources you could point me towards.