With the main event of the world series of poker wrapping up tonight, I thought I’d throw a wet blanket on the dreams of aspiring poker players by looking at the risk-adjusted payoff of entering this tournament. The results are worse than I expected. The entry fee to the main event is $10,000. However, the prize payouts average only $9400 per player. Without any risk adjustment the average player is losing $600 by entering the tournament. To an insurance company with billions in assets, this analysis makes sense. But to people of more modest means, a reasonable amount of risk aversion makes the loss much higher. A sensible level of risk-aversion involves treating gains and losses geometrically. This means that doubling your net worth from $100,000 to $200,000 is as good as it is bad to have it cut in half to $50,000. Based on this model of the utility of money, a person with a $100,000 net worth expects to lose $5918 playing in the main event if his tournament result is just...

Some of the spots at a $1 million buy-in poker tournament called the Big One were won by players playing and winning satellite events. These players are then faced with a difficult choice: play the Big One for a shot at many millions, or sell the spot for as much as they can get. The dollar amounts are definitely life-changing, and it can be difficult to make a rational choice. How much is a spot in this tournament worth? If there are 45 players, the payouts for this tournament go to the top 9 players: $17,200,002.15 $9,480,001.19 $4,080,000.51 $2,480,000.31 $1,720,000.22 $1,520,000.19 $1,320,000.17 $1,160,000.15 $1,040,000.13 The bottom 36 players get nothing which makes the average payout $888,889 (the rest of the buy-in, $111,111, goes to the charity One Drop). So, one answer to the question is that a spot in the tournament is worth $888,889. But this ignores two important factors: 1. Not all players have equal skill. 2. Looking at the arithmetic average payo...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. Some financial decisions, particularly about insurance, must take into account what is called the utility of money to get the right answer. Normally the concept of utility is explained in very mathematical terms, but it doesn’t have to be. Let’s take a fun example straight from a game show. You’re standing beside Howie Mandel playing a super-sized version of Deal or No Deal. You’re down to just two amounts left, 1 cent and $3,000,000! You get the following offer: take $1,000,000 now, or take a 50/50 chance at the $3,000,000. What should you do? If you got to do this many times, then on average, taking the chance you would win half the time and get an average return of $1,500,000. This is more than the million dollars you were offered, and so you should take the chance, right? Not so fast. Most people would correctly figure out that they should just...

Happy Canada Day! This is a special Canada Day version of the usual Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. Insurance is a financial matter and doesn’t actually do anything to prevent accidents. So, if insurance is just about trading money back and forth, how can it be a good deal for both the insurance company and the person buying the insurance? When it comes to buying goods like food, it is easy to see why an apple is more valuable to a person buying one than it is to the farmer who owns an orchard full of apples. I’m quite happy to part with 50 cents for an apple when I’m hungry, and farmers are willing to take less than 50 cents for each of their apples. So, in this case, it is possible for both sides to win. When it comes to insurance, it isn’t as obvious that both sides can benefit. To keep things simple, imagine that a car insurance company has worked out that they will have to pay out an av...

Most commentators advise investors to shift money from equities to fixed income as they age, and this makes sense. We may disagree on the exact asset allocation percentages and exactly how soon before (or after) retirement to start lightening up on equities, but it seems clear enough that the average 40-year old should have more in equities than the average 80-year old. However, there is a body of academic work that argues that investors should maintain a constant asset allocation regardless of their age. This work is based on what is known as constant relative- risk aversion (CRRA). I’ll show the problems with CRRA in an example below. One consequence of the CRRA assumption is that the optimal asset allocation percentages remain constant regardless of the length of the investor’s investment horizon. Paul A. Samuelson advocates this view in his keynote address to “The Future of Life-Cycle Saving and Investing” conference. I first heard of this conference and the correspondin...

In an earlier post I was looking at what fraction of your portfolio should be in stocks. I also listed Larry Swedroe’s table of time horizon vs. stock percentage from his book “Rational Investing in Irrational Times”. His table basically says to put everything in stocks if you won’t need the money for 20 or more years. The stock percentage then drops steadily to zero when you are three years from needing the money. I’ve been looking for some justification for this advice. The answer comes from considering the utility of money . The basic idea of utility is that the wealthier you are, the less an additional dollar is worth to you. An Example Suppose that if you invested your entire portfolio in risk-free investments, you would have $1 million when you retire. A game show host then makes you the following offer. You can just take the $1 million or you can toss a coin to get either $800,000 or $2 million. Would you take the sure $1 million or would you take the chance? What I r...

Some financial decisions, particularly about insurance, must take into account what is called the utility of money to get the right answer. Normally the concept of utility is explained in very mathematical terms, but it doesn’t have to be. Let’s take a fun example straight from a game show. You’re standing beside Howie Mandel playing a super-sized version of Deal or No Deal. You’re down to just two amounts left, 1 cent and $3,000,000! You get the following offer: take $1,000,000 now, or take a 50/50 chance at the $3,000,000. What should you do? If you got to do this many times, then on average, taking the chance you would win half the time and get an average return of $1,500,000. This is more than the million dollars you were offered, and so you should take the chance, right? Not so fast. Most people would correctly figure out that they should just take the million dollars. The reason is that the first million would make a huge difference in their lives, and an additional two mil...

In my last post, I discussed how insurance is a financial matter and doesn’t do anything to prevent accidents. So, if insurance is just about trading money back and forth, how can it be a good deal for both the insurance company and the person buying the insurance? When it comes to buying goods like food, it is easy to see why an apple is more valuable to a person buying one than it is to the farmer who owns an orchard full of apples. I’m quite happy to part with 50 cents for an apple when I’m hungry, and farmers are willing to take less than 50 cents for each of their apples. So, in this case, it is possible for both sides to win. When it comes to insurance, it isn’t as obvious that both sides can benefit. To keep things simple, imagine that a car insurance company has worked out that they will have to pay out an average of $600 per driver in claims for car accidents next year. If they charge each driver $1000 for the insurance, then they will make a $400 profit on each driver min...