I begin with a beautiful illustration from William J. Bernstein’s book, The Four Pillars of Investing. I will quote him directly here to be sure to not take credit for his ideas.
Imagine, for example, that the US Treasury issues a bond yielding 3% in perpetuity – that is, it never matures. Typically, a single bond has a face value of $1,000, so this one yields $30 in interest per year. Now imagine that instead of yielding $30 each and every year, the Treasury secretary flips a coin: heads, that year’s interest is $60; tails, it’s zero.
Clearly, the average expected return for either instrument is 3% or $30 per year. But as an investor, there is no reason to believe that the second instrument will leave you better off than the first, and the first one is much easier to plan around. As a result, demand for the first bond will be greater than the demand for the second, and this will be reflected in the market prices of these two instruments. Perhaps this difference in demand levels results in the second bond being available for $750, instead of $1000. At that price the yield increases from 3% to 4% because 30/750 = 4%. That extra 1% can be referred to as the risk-premium. After this happens we will say that the market is “pricing” the risk of the second bond to match risk and return. Notice that no one actually sets this price, it is simply a realization of supply and demand for products offered in the same market.
Bernstein also lays out a more complex illustration. Consider a setting involving a choice between two retirement accounts. The first account guarantees a 3% return each year. The second account involves an annual coin flop. If it comes up heads – you get a 30% return, but if it comes up tails you lose 10%. Let us also assume that your time to retirement is 35 years, and that each year the employer adds $5000 to the account balance on your behalf.
If you choose Option 1 you are guaranteed to end up with roughly $300,000 after 35 years. This would be $175,000 in the contributions and another $125,000 in interest. If you select Option 2, then over 35 years, you are likely to end up with something like 17 heads and 17 tails. If you could alternate Heads and Tails then each 2 year period would yield 1.3 * 0.9 = 1.17 or 17%. Note that this would be the same as having a guaranteed return of 8.17% per year. This is a lot better than the 3% we discussed above, but there is a catch. The probability of you seeing alternating Heads and Tails for 35 years is extremely small. (About 0.5^35 = 2.9 * 10^-11, or 0.000000003%.) You are equally likely to see Tails 35 times in a row and end up with, $43,748. Of course, you could also see Heads 35 times in a row and end up with roughly $162 million. The central point is that under Option 1 you have a definite end-point, which is a constant value to anchor on and plan around. Under Option 2 you have a distribution with a maximum, a minimum, a mean, and a variance.
The FUNDAMENTAL problem is that for most people the 10% loss that you have when the coin comes up Tails “FEELS” about as bad as the 30% gain that you see when the coin comes up Heads “FEELS” good. As a result, many people implicitly select Option 1 over Option 2 sooner or later. I use the word “implicitly” because almost no one will choose Option 1 sitting here reading a blog or looking at a spreadsheet showing “hypothetical” outcomes. What is much more likely is that someplace along the line you will see Tails 2 or 3 times in a row and run away, stopping the game and getting stuck with Option 1 for the duration of your time. You will probably move your money into Option 1 if you can as soon as a few “bad” outcomes appear back to back in a state of panic — And that, my dear friend is a big part of the reason most people will never be rich.
In the face of a bad outcome you panic and move to the option that brings certainty. Obviously, you never would have considered Option 2 unless the expected return was much better. Even if everyone chooses Option 2 up front, the ability to switch when things get tough creates a collection of outcomes where the realized returns roughly match the risk taken. In other words, the market will look like it matches risk to return even though each individual investor started with the same risk and ended up with different returns.
These numbers may seem arbitrary, but they are not. A broadly diversified portfolio of equities may see an average total return (including dividends) of close to 12%. (It will be closer to 10% if you only use an S&P 500 index.) But you will also see about an 18% standard deviation. (Again, a little less if you restrict yourself to the S&P 500.) Notice that this implies that the mean plus or minus one standard deviation gives you a range of +30% to -6%. Thus, our example using +30 and -10 are in the ballpark. You should also note that the expected return of 8.17% that we calculated above includes the 3% that was guaranteed as an alternative plus something extra. This difference of 8.17 – 3 = 5.17% is very close to the risk premium for Stocks when compared to T-bills currently observed in the marketplace for financial products. You should also note the fact that this spread is remarkably consistent across both time and geography. We have seen a premium in this range all over the world over the past 100 years. There are brief exceptions during extraordinary times such as world wars and pandemics, but even in these settings the long term average quickly returns to the norm. This implies that the size of this premium is not a result of US policies. It’s a side effect of human nature. In fact, I have argued elsewhere that it’s actually much deeper than that. Mammals are risk-averse – not just humans. (See https://chesterchambersphd.com/the-origin-of-risk-aversion)
The universal nature of risk aversion plays out in every financial market. As long as this remains true, it will manifest itself in the supply and demand function of every financial instrument. As a result, prices for those instruments will be a function of that aversion. Ultimately, this means that risk and returns will ALWAYS be positively correlated, even though no real effort is made to make it so.
Please note that I said, “Correlated”, not “Dictated.” Go back to my retirement account where the investor flips a coin and gets a 30% return when it comes up Heads. About 1 out of every million investors will see Heads 20 times in a row. If the employer adds $5000 each year to the account, this balance will reach roughly $4 million after 20 years.
I am thoroughly convinced that this lucky investor will become a best selling author of “How I Beat the Street” or some similar sounding tome. Why not? In fact, with a workforce of 100 million people, there will be roughly 100 of these folks floating around at any given time – and that’s just in the US. This will create a litany of voices screaming about how easy it was to do – “and you can do after buying my new book for only $39.99!!!!” Of course, that’s when those guys really get rich. They will tell you all of the usual stories about how to time the market; how to pick the winners; and how to retire today using my “proven” method.
What they will not do is change human nature, or evolutionary biology. As long as humans dominate capital markets, they will bid up the prices of assets that show reduced variance and be eager to sell those with higher variance sooner or later. Given any set of cash flows, paying more for it after the crowd has bid up the price will ultimately mean you get a lower return. At the same time paying less for it up front means you will get a higher return. As a result, risk and expected returns will go hand in hand even though there is no central planer fixing the prices, and a thousand voices constantly scream that it isn’t so.
Will there be exceptions – of course there will. I never said risk will perfectly match returns. But on average, these two (Variance and Expected Return) have to go hand in hand because human nature is remarkably consistent. That’s why betting that you will beat the market, or get a reward that does not match the risk is a bad gamble. Ultimately, that’s all that we can say.
