Sunday, July 25, 2010

Risk and Reward

"Fortune favors the bold"
-Latin proverb

A CD at a bank is the quintessential risk-free investment.  You give your money to the bank, and the bank guarantees that they will give you your money back with interest at some future point in time.  Even if the bank goes out of business, the Federal Deposit Insurance Corporation (i.e. the U.S. Government) will guarantee that you get your money.  The only way that you will not get your money is if society as we know it collapses. 

[Astute readers might argue that there is risk because if interest rates rise before the CD comes due, you will miss out on the opportunity to invest your money at the higher rate.  This is very true.  However, when I use the term risk, what I mean is that there is no variation in the amount of money that you will get in the end.  If you invest $100, and the CD rate is 2%, you will get $102 99.99999% of the time.]

Let's assume that the one year rate for your CD is 2%.  Now let's assume that somebody comes along and offers you the following deal.  You give him $100 at the beginning of the year.  Then at the end of the year, he flips a coin.  If it comes up heads, he will give you 2% interest or $102; however, if it comes up tails, he will take all of your money.  Will you take this deal?

Until you are totally insane, you would never take this deal.  Why not?  Because you can get the same $102 by investing in a risk-free CD.  Why would you take a chance at losing your $100 just for the opportunity to get the same $102 that you could get from a CD?

Now let's say the person amends the deal.  You still lose all of your money if the coin comes up tails, but if it comes up heads you will double your money and get back $200.  Do you take this deal?  Because the payoff is much higher, you just might take it.  Yes, there is a chance that you will end up with $0.  On the other hand, if you are fortunate, you will end up with a much bigger payoff than if you put your money in a CD.

Which is the better option?  It all comes down to your risk tolerance.  If you are counting on that money for something, you might not want to take the risk despite the possible rewards.  However, if you are willing to take a chance, it just might pay off.  The point here is that in order to get you to take that additional risk, the person offering the deal needs to make the payoff higher than what you could get if you took no risk.

This rule can be summed up as follows:

The greater the risk, the greater the possible reward needs to be.

This is illustrated graphically below:

Risk vs Expected Reward

The left end of the line shows the expected reward when there is no risk.  As you move right along the line, you will see that the risk is increasing, but the expected reward is increasing as well.  This relationship forms the basis for all investing decisions.  An investment needs to compensate you for any additional risk.  If it does not, then don't invest!

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