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Alpha Theory Blog - News and Insights

« September 2009 | Main | November 2009 »

3 posts from October 2009

October 30, 2009

Knowing the Financial Spread - Investor Lessons from WhatIfSports.com

“Once The Star-Spangled Banner began to play, I’d tell myself, “Here you go.  Start pulling away, start computerizing.  You must think clearly and remove yourself”...It was like watching a game through a window.” – Bill Walsh, Head Coach of San Francisco 49ers and creator of the West-Coast offense

A buddy of mine who knows how much I love sports analysis, sent me a website called WhatIfSports.com that runs mock simulations of games 10,000 times to create a projected outcome. Now I have no idea about the efficacy of WhatIfSports's Monte Carlo simulation, but I love this kind of stuff as anyone that has spoken to me about the chance of the Tarheels winning the National Championship in basketball can attest (we’ll save that diatribe for another blog). So, I decided to see what the best way to profit from this simulation, assuming it was accurate. I pulled up Vegas odds and Whatif’s NFL week 8 projections to see if I could find any inconsistencies and did a quick analysis: 

WhatIf

Based on this, Vegas was pretty much dead on, but not perfect. How would I profit from these mis-priced games? I would definitely bet the under on the Falcons/Saints, because Vegas has the game total at 54 and WhatIfSports has the total at 45.  I would also pick the Rams getting 9.5 points over the Lions, when WhatIfSports has the Rams winning outright. I may also pick the Broncos and 49ers, but I would not be as confident and would certainly place a smaller bet on those games. This got me thinking about how this analysis applies to investing.

If I am evaluating a basket of stocks for potential investment, the Vegas Odds are the current stock price because they indicate what I can “buy” the bet for today and the WhatIfSports analysis is my proprietary research. I want to find the assets with the biggest differentials, Falcons/Saints under and Rams and make big bets on them. If I find other stocks with a reasonable difference between the market price and my calculation of value then I will place a bet on them as well, but not to the same degree as the large spreads.

If I’m an investor, how can I determine which assets should go in my portfolio and how to size them without calculating the risk-adjusted return of every investment? I must measure the difference between the market price and what I think the value is to determine the attractiveness of the bet. This concept seems so straightforward, yet most investors are willing to allow their mental calculator to be the final arbiter of portfolio inclusion and position size. That’s just like looking down the list of Vegas Odds and saying, “hmmm, I know the Saints score a lot and 45 isn’t that high, I think I’ll take the over.” First off, our brains are not very well designed to make those kinds of decisions, just read any book on behavioral finance or neureconomics. Second, even if you are right in your assessment that it is a good bet, how do you know exactly how good it is. Is it pretty good, really good, or freakin’ fantastic? Those differences affect how the position should be sized.

No doubt, calculating risk-adjusted return is harder than not calculating risk-adjusted return. But honestly, there are millions/billions of dollars at stake. How do you know what to bet if you don’t know your own spread?

So, wish me luck this Sunday and GO RAMS!!!

October 27, 2009

The Probabilistic Theory of Relativity

“A reasonable probability is the only certainty.” – Edgar Watson Howe

In Einstein’s Theory of Relativity, he postulates that space and time are relative to the person observing them. That a set of twins, one standing here on Earth and the other shot at the speed of light to the edge of the universe and back, will be significantly different in age when the twin returns to Earth, even though neither one of them noticed a difference in how time passed. In fact, if I take off on a cross country flight and my wife stays at home, I will be slightly younger than her when I arrive on the West Coast. In these examples, time and space are not continuums rather they are experiences. Careers are devoted to understanding Einstein’s theory, so we will not go into the science here, but understanding relativity is important for us as investors.

Knowledge itself is relative. I do not know if a company I’m invested in will beat earnings but the CFO surely does. In this case, uncertainty becomes relative and dependent on our differing levels of knowledge. If I, the investor, am assigning a probability of the company beating earnings, I will base it on my compiled knowledge of the company. As my knowledge changes, I will change my probability of success. The CFO will do the same thing, but his base of knowledge is different. This is described in statistical parlance as epistemic probability. Epistemic is the antagonist of aleatory probability (i.e. coin-flips) which is described by statisticians as an uncertainty due to randomness. No matter how much knowledge I gain, I will never know the outcome of a coin-flip, only the probability of its outcome.

Investing is not like coin-flips, blackjack, or poker in our ability to define aleatory probability. But that does not mean that we should give up on estimating an epistemic probability. In fact, it should be the foundation of our investment process. Gene Gigerenzer describes Degrees of Belief in his book “Calculated Risk”, “The point here is that investors can translate even onetime events into probabilities provided they satisfy the laws of probability – the exhaustive and exclusive set of alternatives adds up to one.  Also, investors can frequently update probabilities based on degrees of belief when new, relevant information becomes available.”

In investing, you are forced to invest with the knowledge you have today. There are no certainties and, as a result, we must accept that every investment thesis is based on a probability (degree of belief) of an outcome. For examples sake, let’s say that our degree of belief is 80%. This creates a vacuum that can only be filled by describing outcomes that make up the other 20%. In this vacuum, lies the elegance of probabilistic investing. It is an imperative calculation for every investment because it requires you to consider all the possibilities and it provides the flexibility to incorporate ever-changing research.

October 07, 2009

The Probability Problem

“The fundamental law of investing is the uncertainty of the future.” – Peter Bernstein, famed investor

 

I am offered two bets. In bet number one, I am paid $150 for every heads and pay $100 for every tails. My risk-adjusted return is 25%. In bet number two, I’m presented with a bag of poker chips that are only black or white. I’m paid $150 for each white chip I pull out and I have to pay $100 for every black chip I pull out. I don’t know the distribution of colors, so my probability assumption would be 50/50. Drawing poker chips also has a 25% risk-adjusted return. Would I be equally likely to make both bets? No, I prefer the coin-flip bet because I am more certain about the distribution of probabilities.

 

To try and balance this issue, let’s assume that we could, with reasonable certainty say the range with which our poker chip probabilities would fall. In this example we’ll assume that white chips are somewhere between 30% and 70% of the contents of the bag. This widened distribution takes into account my uncertainty regarding my probabilities. Unfortunately, if I plot out every payout between 30% and 70% probability of success, I get an average of 25%. I’m back at square one.

 

What about betting systems that constrain loss? If I use Optimal-F (Kelly) suggested bet size, I get 17% bet for the coin-flip, which is the same as the average of all of the Optimal-F bets between 30% and 70% probability. Alpha Theory optimal position sizes suffer the same issue with a position size equal for both coin-flips and poker chips.

 

Here is my simple solution until I understand a better Bayesian solution. I have a somewhat arbitrary Analysis Confidence rating. Let’s name them High, Medium, and Low. The coin-flip is definitely “High Confidence” because I am certain about my coin-flip probabilities. The poker chips are “Low Confidence” because I know nothing about their true distribution. But my knowledge about the poker chips is not static. The probabilities are epistemic because, as I draw more poker chips, my knowledge of the distribution of chips will improve. I will adjust my probabilities as I draw chips and change my Analysis Confidence from Low, to Medium, and eventually to High when I have a better grasp on the distribution of chips in the bag. To account for uncertainty, I’m going to cut my bets. If I have Low Analysis Confidence, I cut my suggested bet in half, if I have Medium I cut it by 25%, if it is High, I don’t cut my bet at all. This is certainly imperfect, but it does create the effect we are shooting for, less exposure when we have less certainty in our assumptions.

 

This, of course, applies to equity investing. You may have high certainty in your probabilities for one investment and only low certainty in another. They both may have the same Risk-Adjusted Return, but you are not willing to invest in them equally. Use the same Analysis Confidence constraint to adjust position size and apply a heuristic-based cut since probability theory does not have a better answer. Alpha Theory provides an Analysis Confidence setting for precisely this purpose to better refine position sizes beyond Risk-Adjusted Return.