The WPF Coin Flip Risk Assessment

Disclaimer Reminder: I am not a financial advisor. This blog nor the author is responsible for investing decisions you make. Please consult with a professional before investing. You can find our full disclaimer here.

Nobody wants to lose money!

Psychologically, it hurts much more to lose than it feels good to win. Think about how you would feel taking $1K out of an ATM and then having it fall out of your pocket. Now think about how you would feel to learn everyone at your company including yourself were given a $1K (net of tax) bonus at work. Personally, I’d be much more upset about losing the cash than happy about the bonus.

Even though it hurts more to lose than to win, remember that in equal amounts, they have the same financial effect! Is this fear of loss holding you back when you invest?

Coin Flip Risk Assessment

Pretend you walk into a casino and are given an opportunity as a new customer. You can bet $1,000 on a (fair) coin flip. You need to risk $1,000 of your own money from your taxable or retirement investment account. Any winnings would go right back to the same account. You have a 50% chance to win. If you call the flip correctly, you win 2x your bet plus your initial wager back, a profit of $2,000. If you call it wrong, you lose your $1,000 wager. You can only play once. Your expected value (EV) is the average result of the bet based on the odds. Almost every standard casino bet leaves you with a negative EV. That’s why the house always wins. In our risk assessment, your EV would be a profit of $500.

[EV=(2,000*50%)+(-1,000*50%)] Would you take this bet?

Result Profit/(Loss) (a) Probability (b) EV=a*b
Win 2,000 50% 1,000
Loss (1,000) 50% (500)
Expected Value (EV) 100% 500

When You Should or Should Not Take the Bet / Make An Investment

The bet is effectively a high variance way of earning an expected $500 for 1 minute of your time. Personally, I’d be more scared to give up the opportunity for $500 of EV than scared to risk $1,000 of my money in order to win. There are 2 important factors leading me to the decision to take the bet:

  1. I have an expectation of a strong return on investment for the bet. The expected return of $500 is the best option available for my money in the brief time it would take to make this bet.
  2. I can afford to lose the $1,000 if it does not work out. My net worth is well over $1,000. If I lost, it would not change my life much at all.

Not having $1,000 to lose is the only reason I can see passing on the bet in this example. If losing $1,000 won’t impact your life and you don’t want to take the bet, think about why. If you don’t have $1,000 to lose, try the same test with $100 or $1 to see if your decision to pass was based on the amount or your unwillingness to take on risk. Is your aversion to risk holding you back?

Don’t Fall For Marketing Gimmicks

By the way, casinos really do occasionally have these 2x bet offers in the form of match play coupons. Usually, they will give a couple of coupons to match your bets. Here at Winning Personal Finance, we play to win. If a casino gives us 10 match bet vouchers, we would play exactly 10 hands of blackjack (or whatever game) and then put the profits in our pocket and walk away.  As soon as we are out of vouchers, we leave. In the end, we would make 10 profitable bets and 0 unprofitable ones. As investors, our goal is to accept risk only when it gives us an acceptable expected return on investment for the risk accepted.  If you have the discipline, playing the 10 vouchers and walking away is a solid winning plan. Many gamblers don’t have this discipline. They keep playing after the vouchers are done and don’t leave until all their money is gone. Isn’t marketing great?

Evaluate Your Tendencies and Accomplish Your Goals

I try to invest as efficiently as possible in order to minimize the time that it will take for me to accomplish my financial goals. The purpose of this post was to make you think about your natural inclination towards risking money in an investment. If you would pass on the hypothetical coin flip, you may be too conservative in your investment choices. My next few posts will continue to focus on the topic of risk in relation to investing in the stock market. Like everyone, I’m afraid of losing money on my investments. However, I’m also afraid of my money losing purchasing power (due to inflation) and missing growth opportunities if I choose not to invest.

Think about your natural tendencies. Are you risk averse? Consider how your money is invested. Do you have too much money (that you don’t need in the short term) kept in “safer” investments such as cash or bonds instead of stocks due to fear of loss? Are you avoiding risk and therefore costing yourself expected value in the long run? How much longer will it take you to accomplish your financial goals because you fear losing?

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