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Geoff Garbacz James DiGeorgia

Education Corner, Options - There's Risk in Reward

April 20, 2006

There's Risk in Reward

Over the past few months, I've presented some hedging ideas and strategies for retail investors. Many of the questions I receive have a similar tone where people ask things like, "Wouldn't it be better to buy the $50 call instead of the $55?" or "Wouldn't it be better to sell a higher strike put so that you get a bigger credit?" While these are great questions, there is one simple way to answer them all decisively — by understanding the elusive concept of risk versus reward.

Many people who claim to understand risk and reward still fall into traps with options. So I want to take a little detour this week and present a quick review of what risk and reward is all about and explain why it exists. One of the best ways to understand risk and reward is to follow along with a simple game that we present in many of our seminars.

Suppose you are given the opportunity to bid on three games. The highest bidder is the winner and is allowed to play the game just once. If he wins, he gains the prize but if he loses, he loses his bid amount.

The first game is simple; you're guaranteed to win $100:
[Image 1]
Think about it for a moment. How much would you bid to play this game? Every time we present this in seminars, this game is quickly bid up to about $99 or higher. And why not? As long as the bid price is less than $100, the winner will definitely walk away ahead, which offers a strong incentive for players to win and therefore bid high.

In the second game, the winner is determined by the flip of a coin:
[Image 2]
If it lands "heads," the highest bidder wins $100. If it lands "tails," the bid price is lost. How much would you pay to play this game? Even though the $100 prize is the same, the second game involves some risk. In the long run, players win half the time and lose half the time. Because the high bidder is only allowed to play once, they are not as eager to play and bid more conservatively. Even though the "fair value" of this bet is $100, we rarely get more than $49 when presented in seminars.

For the third game, we take a well-shuffled deck of cards:
[Image 3]
If you select the ace of spades (no peeking, of course), you win the $100 prize; otherwise you lose your bid amount. In this game there is a considerable amount of risk. On average, you will only win this game once in fifty-two tries. We rarely get more than 25 cents for this game (even though the fair value is $1.96).


We can take the high bids for the three games and present them in another way. We could say the winner of the first game is willing to pay $99 in order to make $1, which is a very low percentage return. The winner of the second game is willing to pay $49 to possibly make $51, which is a much more attractive return. And the winner of the third game is willing to bid 25 cents and may make $99.75, which is a stellar return.

Which game would you prefer to play? When presented in this way, most people want nothing to do with the second and third games, which is demonstrated by the fact that they are often bid far below their theoretical values. Now think about these two investments (with all else being the same):

• An option spread trade that costs $4 and can make a maximum of $1
• An option spread trade that costs $1 and can make a maximum of $4

Many people (including professionals) will tell you to definitely take the trade that costs $1. They reason that it is a much "better" risk-reward ratio. On the surface, that certainly seems correct. Why should you pay $4 and only make $1 when you can pay $1 to make $4? But now you know that the answer is not that easy. The reason the markets bid the first option trade up to a "lousy" payout ratio is because this investment has less risk than the second. This option trade is similar to the "guaranteed" game — that's why the price is high and the potential payout is low. The second option trade is much riskier as shown by the fact that the market only put a $1 price tag on it, which leaves it with a $4 reward (similar to the card game).

It is easy to see the "risk" in the first three games since you can clearly see the mechanics of how the money is won. But what if earlier we just said you get to choose between the following three games:

• Pay $99 and make $1
• Pay $49 and make $51
• Pay 25 cents and make $99.75

Now you can see why it would be so easy to want to play the third game — the risk is now hidden. If the risks were the same for all three, there is no doubt that the third game is the best one to play. But there is risk, which is why the prices are different. And remember, you were the one who put those prices there and had a good reason for it! Make no mistake about it — the markets are always calculating risks and bidding all assets accordingly. The risks are there even though you may not directly see them, but they can always be found in the form of risk-reward ratios.

So is it "better" to use one option over another since it increases the amount you can make? Not necessarily. It increases your reward, but it also increases your risk. If you're not willing to take more risk, don't fall into the trap of only looking at the bigger reward.