At its core, investing is about risks and rewards

The Nobel Laureate William Sharpe came up with the Sharpe ratio that helps you compare and contrast different investment options - by considering their risks and rewards

In general, the more risk you take, the more rewards (essentially, returns or yield) you deserve - it’s the foundational framework of investing

**In the first case, imagine you are thinking of buying a stock of NASDAQ**

How would we think about the risks and rewards for this case ?

For that we need to understand Sharpe Ratio first

**So, Sharpe Ratio is (R_i - R_treasury) / standard deviation of (R_i) **

Let’s look at all three elements here :

R_i is the annual average return of the investment you are considering now (NASDAQ)

R_treasury is the annual average return of a ten year US treasury note

Standard Deviation of R_i, is the volatility of the investment’s return over time

**Risk free yield : **It’s intuitive, right ? the US treasury note is generally considered the safest investment in the market by investors in the US and around the world. It’s essentially a risk free investment, it’ll only fail to pay you back if the United States goes bankrupt, and that has never happened in history. The US has also never defaulted on its debt obligation to investors

As far as risk free goes, it is as risk free as it gets

**Why deduct risk free yield from NASDAQ yield ?** We deduct the treasury note yield from the NASDAQ yield (in the numerator of our formula), because we want to find out how much additional yield we’d get by investing in NASDAQ, on top of the risk free yield we would have gotten by investing in a treasury note. Then we would contextualize it by thinking about, how much additional risk we undertook for getting that extra yield

Perfect

Here are the NASDAQ yields for the last ten years

The yield (return) for a ten year treasury note as of now is 4.2%

The average annual yield for NASDAQ between 2014 and 2023 is 19.6% (as you can see from the table above)

The treasury note is a fixed income asset and hence your returns are fixed. But the returns from NASDAQ fluctuate year to year, so to understand the volatility of returns, we need to understand the standard deviation of those returns

**Standard Deviation:** Standard deviation is just a way of understanding how anything varies when compared to the average. Say, you weigh 170, 180, and 190 pounds in year 1, 2 and 3, then on an average you weighed 180 pounds over those three years, with a standard deviation of + or - 10 pounds (this + or - 10 pounds is the standard deviation of your weight)

You can say, over these three years, you weighed 180 pounds on an average, with a standard deviation of +/- (plus or minus) 10 pounds

We can do the same thing for annual returns from an investment to understand the volatility of it’s returns

The standard deviation of the yield for NASDAQ is 25.8%

A higher standard deviation just means your returns move a lot from year to year, just like your weight

Great

**So, Sharpe Ratio is (R_i - R_treasury) / standard deviation of (R_i) **

**Sharpe Ratio for NASDAQ : (19.6% - 4.2%)/25.8% ~ 0.6**

This 0.6 will have more meaning in a moment - as we proceed further

Now let us do the same thing for Bitcoin

The average of annual yield for Bitcoin between 2014 and 2023 is ~ 191%. This certainly is almost 10x of NASDAQ (annual average yield ~ 19.6% for NASDAQ). But that is not the entire story

The volatility for Bitcoin, measured using standard deviation is astronomical and is 419%, which is 16x of NASDAQ

**Sharpe Ratio of Bitcoin : (191% - 4.2%)/419% ~ 0.45**

**In Summary : **

The Sharpe Ratio of NASDAQ is 0.6, and for Bitcoin it is 0.45. Bitcoin certainly provides almost 10x the returns as NASDAQ on an average. But, because of those huge swings in Bitcoin prices from time to time, its volatility is 16x as much as NASDAQ, and hence it ends up with a lower Sharpe Ratio, when we consider risk

In terms of risk adjusted yield, NASDAQ is 25% better than Bitcoin. Another way to say the same thing - for you to choose Bitcoin over NASDAQ, given its volatility, Bitcoin needs to give you more than 191% return in annual yield

It makes sense intuitively right ? Bitcoin is just Bitcoin, whereas NASDAQ Composite Index has 2,500 firms in its index. If Apple has a bad year, NVIDIA will pick up the slack, or AMAZON will rescue your portfolio, but if you have only one asset in your portfolio, the risk is intolerable

I am all for new technologies, and new and innovative ways of organizing our world, and crypto currency definitely has unlimited potential. However, it is still a working product as the world finds large scale use cases for it

I believe in intelligent investing, which precludes me from being a religious crypto broseph. I am not religious anything, if I can sell llamas or alpacas and make money in Manhattan, I happily would, as long as its within my tolerance for risk

**Risk adjusted yield** is one of the ways to compare returns from two investments with wildly different risk profiles

‘tis not just about how much you got in yield, it’s about how much risk you took to get that yield. You can certainly build a taller Jenga tower, but the higher it goes, if you don’t manage risk, it might all come crashing down

Sources : Slickcharts (NASDAQ Returns), Bankrate (BTC Returns) and NASDAQ Composite Index