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March 26, 2023

Risk and Reward

Will Rogers once said, "Why not go out on a limb? That's where the fruit is." This is one of the simplest ways of expressing the relationship between risk and reward. He was, of course, referring to the fact that in order to get the fruit (reward) you must venture out onto the tiny, unstable limbs. In other words, you must take some risk. The same concept applies to every financial decision you will ever make. In financial terms, if an investment is risky then we mean there is a chance you might lose some or all of your initial investment. The greater the chance for loss then the greater the risk of the investment.

Risk and reward is the inseparable dynamic duo of finance and always increase and decrease together. If the potential reward from an investment is great, you can be sure that it comes with a lot of risk. And if the risk is low, you can forget about making a lot of money.

While the concept of risk and reward may make intuitive sense, it is one of the most overlooked concepts among investors and causes many problems for those who only consider the reward side. If you want to succeed in investing, it is crucial that you understand the risk-reward relationship and why this pair cannot be separated. We can easily convince you why risk and reward go hand-in-hand by playing a simple game.

Pricing Game

Imagine that you are offered the chance to play the following three games. An auction is held to play each game. The highest bidder is allowed to play the game one time and does not get his bid amount back. If you win, you get a $100 cash prize. Think about each of the games and then jot down your answers on a piece of paper:


1. For the first game, the highest bidder is guaranteed to win $100 cash. No risk. No hidden strings attached. If you are the high bidder, you walk up and collect $100. How much would you bid to play this game?


2. For the second game, you must correctly call heads or tails at the flip of a coin in order to win the $100 prize. How much do you bid to play the game now?

deck of cards

3. For the third game, you must draw the ace of spades from a well-shuffled deck of cards in order to win $100. How much would you pay to play this game?

Even though we don't know the particular answers you chose for each game, we are 100% certain that you elected to pay the most for the guaranteed game, the next highest amount for the coin game, and the least amount for the card game. How do we know this? It's because of the relative risks involved in each game. The first game has no risk; we know that the winner always wins $100. And because of this, most people will bid this game up fairly close to the $100 reward. For the coin toss, we know that you would win $100 half the time and lose half the time, which is certainly not as good as winning all of the time. In other words, we are less confident in the outcome - there is risk. There is no chance of losing with the first game but a significant chance of losing with the coin game. Because of this, you should be willing to spend less for this game. For the card game, we know you would win $100 only once out of every 52 tries, on average. This means you are almost certain to lose your money. On a comparative basis among the three games, this is the riskiest so you should be willing to spend the least to play it.

We just reviewed each game in terms of risk and find that the higher the risk, the lower the price you are willing to pay. We can look at the three games in a positive light as well and say that the more desirable the game, the higher the price you should be willing to pay. The guaranteed game is more desirable than the coin game and that's why its price is higher. Or conversely, the coin game is riskier than the guaranteed game so it is cheaper.

It doesn't matter which dollar amounts you picked for each game but, just for the example, let's assume you bid the following amounts:

Guaranteed game: $99

Coin game: $49

Card game: $1

Once we have some prices to work with, we can look at the three games in a different way. If you were willing to pay $99 for the first game, that's the same thing as saying you were willing to invest $99 in order to make a $1 profit. The coin game, on the other hand, represents a game where you could invest $49 for the chance to make a $51 profit while the card game represents an opportunity to invest $1 in hopes of making a $99 profit.

Notice the relationship between the prices and the rewards: The higher the price, the lower the reward. The guaranteed game carries the highest price of $99 yet comes with the smallest reward of $1. The coin game has a bigger reward and a correspondingly lower price. The card game has the biggest reward of all and also has the lowest price.

The reason for this price and reward relationship should now be obvious to you. It is solely due to the risk of each game. The bigger the risk, the less you are willing to pay, and that allows for a bigger reward.

Price is the Equalizer

The market places a lower price on riskier assets as a way to equalize the risks. In the pricing game, you placed a higher price on the coin game than the card game. This doesn't mean that the coin game is necessarily the better game. If the coin game and card game were priced the same, then we could say for sure that the coin game is better. After all, it wouldn't make sense to pay the same price to play the card game. But because there is more risk with the card game, you will bid a lower amount. Once the prices are established for all three games, then all games are theoretically equally attractive. Your decision on which one to play just depends on how much risk you wish to take (or on how much reward you're looking for). If you don't like the $51 payoff of the coin game, you can certainly jump to the card game and go for $99. But just understand that this decision means you are taking more risk and therefore have a higher chance of losing your investment. You cannot jump to a better payoff and take less risk. If you want more reward, you must be willing to take more risk.

As you build your investment portfolios, it's important to never forget the risk-reward relationship. However, investors and traders unintentionally neglect it all the time and it causes many losses and misleading beliefs.

For example, many investors think that you're better off buying low-priced stocks since a $1 gain represents a much bigger percentage return on your money. If a $1 stock rises $1, then you've doubled your money. But if a $100 stock rises $1, then you've only made one percent on your money. Many traders assume that the $1 stock is therefore the better investment. After playing the previous pricing game, you hopefully understand why that's not true. Both stocks have a chance of making a $1 gain just as any of the pricing games had a chance of making $100. But as the chance of making the $100 falls, so does the price. And that's why the market will price some stocks at $1 and others at $100. The market places a higher price tag on the investments that are more likely to produce a profit - just as you did with the pricing game. Traders who believe the $1 stock is the better investment make the mistake in believing that both the $1 and the $100 stocks have the same chance of rising $1. And that's an easy mistake to make since we do not have little pictures of a coin or deck of cards next to each investment to remind us of the risk involved. But you can be sure the professionals are assessing the risks of each investment and pricing them accordingly. If you're still not sure, a casual following of some stock quotes will quickly demonstrate that prices of cheap and expensive stocks do not move equally. You will find that stocks in the $100 price range rise and fall $1 all the time for no apparent reason. However, you will never see that type of daily activity on a $1 stock unless there is significant news. The chances of moving $1 are therefore not equal for the two stocks and that's why they are not priced the same.

This is not to say that you should never buy a $1 stock. We're just saying that you should not buy a $1 stock on the belief that it must be better than a more expensive stock just because the percent return would be greater for any given price increase. It's true that the percentage return will be greater but you need to understand that the "benefit" does not come for free. The benefit comes at the increased risk of losing some or all of your money. Investors who do not understand these relationships inevitably make the mistake of continually reaching for the riskiest assets - and also end up taking lots of losses.

Stock Advisors

Understanding this inescapable risk-reward relationship can keep you from being misled by those who tout stocks, strategies, or their stock picking skills. For example, at a recent seminar, the speaker said that investors "had it backwards" because they are, for example, willing to spend several thousand dollars on a stock in hopes of making a few hundred dollars. "Why not," he continued, "spend a few hundred on some options in hopes of making a few thousand dollars." Many traders immediately bought into his idea not realizing that there is a very real cost. The investment in the stock and options are not directly comparable because the chances of losing your few hundred dollars in options are far greater than for losing a few thousand on the stock investment. From the speaker's viewpoint, the options appeared better since he could "pay a little" in order to "make a lot." But notice that's the same relation that you were offered in the card pricing game. With the card game, you could pay $1 to make $99, which certainly sounds like the most favorable risk-reward schedule. Most people would refuse to play the card game; however, they are all too eager to jump into hidden variations in the stock market. The speaker at this seminar was unknowingly getting investors to switch to a riskier strategy. Using our earlier games as an analogy, he was trying to get people to switch from the coin game to drawing the ace of spades.

You'll hear other fallacies too. For instance, some will tell you to stay away from bonds since you cannot make a lot of money. After all, why spend $9,900 on a government bond that matures to $10,000, thus netting you only $100 profit on your investment? The reason that investors do is because it is guaranteed. Because of its no-risk structure, the market places a very high price on that investment. The market does this for government bonds for the same reason that you probably bid very close to $99 to win the guaranteed $1 profit in the pricing game.


Option traders make similar risk-reward mistakes with options. If an option trader wants to buy a call, he will most likely buy an at-the-money or out-of-the-money strike. The main reason traders like these strikes is because they are cheaper than the lower strikes. Once again, traders erroneously assume that all options have equal chances of rising or falling $1 and so feel that it only makes sense to buy the cheapest options. You should now understand that all cannot have equal chances of rising $1, otherwise they would cost the same. The market bids up the prices of the lower strike calls because they are less risky. But if you do not understand the risk-reward relationship, you will be tempted to buy higher strike prices thinking that you are doing yourself a great service by only putting a little bit of money into the trade, which gives the appearance of lowering your risk. The cheaper the option, the higher the risk.

Options can also be used in combination to create limited profit structures. For example, you may hear traders talk about a strategy where they paid $3 that can make a maximum of $5 (a $2 profit). The benefit to limiting the maximum upside is that the price to create the position is much cheaper. But many will tell you they prefer cheaper structures with higher payouts such as one where they may pay $1 to make $5 ($4 profit). They often argue that it is just makes sense because of the "better" risk-reward ratio. The mistake in believing that the cheaper one is "better" is based on the faulty belief that both strategies are equally risky. The cheaper the investment, whether it is a single option or a combination strategy, the higher the risk.


Our basic risk-reward relationship can be found in many other areas outside of the financial markets too. As long as there is a price paid in exchange for a possible financial reward, the risk-reward relationship holds. Take, for example, the state lotteries. Why do you suppose that you can pay $1 for a ticket for the chance to make $7 million or more? The reason is that the chance of making that huge reward is very small and so the price will also be low. It does not mean that it must be a great investment because of the "great risk-reward ratio" that so many traders talk about. If there is a great reward, there is a low price - and also a lot of risk.

The Florida lottery offers two versions of a scratch-off Monopoly game: Super Monopoly and Instant Monopoly. Super Monopoly offers a $100,000 grand prize while Instant Monopoly only offers $5,000. However, both cards cost $1 to play. Does it follow that Super Monopoly is the better game since it is better to bet $1 to make $100,000 rather than $5,000? The answer is no since better payout is a reflection of the higher risk involved in that game. In fact, you can even verify this is true by going to the lotteries website and looking at the odds. For Super Monopoly, the odds are 1:2,520,000 and are 1:890,000 for Instant Monopoly. Although neither odds are good, there is no doubt that, on a relative scale, you are more likely to win at Instant Monopoly and that's why the payout is lower.

Comparing Returns among Funds and Managers

Another reason for understanding the risk-reward relationship is that it will keep you from choosing your investments in a misguided way. You will be persuaded by different types of investments or individual stock pickers to put your money with them because they "beat" the Dow or some other index. While their returns may be higher, it does not mean that they necessarily beat it on a risk-adjusted scale. As an example, assume the Dow increases 10% over the year but a money manager tells you to put your money with him since he earned 20%. On the surface, it seems like he did better. However, we haven't considered the risk. What if this manager invested all his clients' money into Super Monopoly to get the 20% gain? Now it doesn't appear too impressive. If he is taking that much risk, you'd certainly want better than a 20% increase on your money. We'd say that, on a risk-adjusted scale, this manager didn't perform as well as the Dow even though his return is higher. Traders and money managers who place their money in high-risk investments will do better than the Dow or S&P 500 or other broad-based index from time to time. But the chances that they will sustain that record are very low. People who place their money with a fund or manager just because they posted the highest numbers are mistakenly assuming that all of them took the same amount of risk. Before you place your money with them, find out what they are investing in before you get too impressed with the numbers. At any given time, there are thousands of speculators and hedge funds who speculate with high-risk investments. It shouldn't be a surprise that many of them will beat the Dow or S&P 500 during the course of a year. This doesn't mean that they are more skilled than the manager who returns a smaller number.

Make sure you understand the risk-reward relationship before you start investing. Risk and reward never separate. They are joined together by a rational force - the same force that caused you to price the earlier games in the order you did. If you always seek the investments that have the highest potential for return, you are by default, seeking the ones with the highest risk.

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