Understanding Risk for better decision making: creating our own Sharpe Ratios

Decisions are something we have to be aware of and make every single day of our lives. Whether they are small, seemingly unimportant decisions like brushing our teeth or going to bed early, or big ones like choosing a major or declining a job offer, our decisions shape our future and our personality. With every decision comes an outcome… and a share of risk that we need to take into account before making a move. And yes, we all have trouble making big decisions and wish we could understand the situation better… that’s why we’re here today!

In finance, risk means the degree of uncertainty or the probability of failure that’s inherent in an investment decision. When we invest our money in stocks (for example), there is a certain amount of risk associated to those stocks, which means there is a chance we’ll lose our money. The higher the risk, the more likely we are to lose our investment, but the return we can get for our investment will be higher too. Risk can come in many shapes, such as inflation risk or liquidity risk among others, but let’s focus on the definition we’ve just given.

Having to choose sucks.

We know risk is the probability of us losing our money, and we want to maximize our return while minimizing our risk (if this does not suit you, you are a bit crazy!). In the 60s, William F. Sharpe created a way to measure how profitable an investment was according to its risk level, so that we could tell whether a certain asset was undervalued or overvalued, and make our decision based on the result. The Sharpe Ratio works as follows:

E is the expected value of the difference (excess) between the asset return  and the “risk-free” return  (more a concept than a real thing, but we normally use government bonds as an example of “risk-free” assets. We can also use savings accounts as examples of “risk-free” assets).  is the standard deviation of the asset we are analyzing (i.e. the difference between all the possible final results and the central “expected” value). If our asset’s risk is very low and the return is very high, its Sharpe ratio will be very high as well, and vice versa. Therefore, when comparing several assets, we’ll choose the one(s) with the higher Sharpe ratios.

Back to real life now. How is this helpful for us? I know many of our decisions don’t involve assets or money in general, but we can create and use our own Sharpe ratios to weigh the pros and cons of every decision. Here is an example I’ve come up with to explain it better:

“You want to impress a girl you’ve talked to two or three times at school by playing a very romantic song on the guitar, which will take you about 15 hours of practice. That’s about a week if you practice 2 hours every day, but you need those 2 hours to study for your finals. You know most of the syllabus already and it won’t make a great difference for you, maybe 1 or 1.5 points over 10; you are 100% sure you’ll pass but getting an A+ looks very appealing to you. Do you go for the girl or do you stay at home studying?”In this scenario, we have a “risk-free” asset: you are going to pass the exam no matter what (you’re not going to lose money) but you can invest your time in trying to get a better grade (is that really a low return? I’m not that sure now :D). On the other hand, there is this cute girl you don’t know much about, but you think you can win her by investing your time in learning a song and playing it for her. As you can see, there is a lot of uncertainty and it all comes down to how much better you think the girl is compared to the A+. If you are, like me, quite risk averse, you’ll stay at home and try your luck after your finals, but you can be a risk seeker and choose to jump in the deep and see how it goes. What you have learned in both cases is how to measure risk and return.

The key to understanding how to make decisions the Economic way is to know and predict every possible outcome and choose what suits your risk profile better. You’ll always have your “risk-free” asset, which is not making a decision, but even that decision of not making any decisions will get you to an outcome and you must add that scenario to the equation in order to have an unbiased view of your problems.

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