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- In statistics, the null hypothesis is the default statement that you test with data. From this test, you can either reject the null hypothesis in support of an alternative or assert that there is not enough evidence to believe anything other than the null hypothesis with a certain degree of confidence.
- In an industry driven by speculation and talking heads pushing the next hot investments, an appropriate null hypothesis for investing is that, “the market is probably right.”
- Starting with this null hypothesis is a way to temper hubris with humility. After all, if earning excess returns in an investment were easy, everyone would be doing it.
- As investors prepare their portfolios for 2018, accepting that our evidence may be nothing but a fortunate permutation of randomness allows us to adequately hedge our confidence and design a portfolio that is robust to our hubris.
In statistics, the null hypothesis is the default assumption: our base case scenario that we assume is true. Our aim is to propose an alternative hypothesis, examine the data, and then determine if there is sufficient evidence to reject the null hypothesis in support of our alternative.
For example, our null hypothesis may be “value investing generates zero expected excess return.” Our alternative hypothesis, then, would be “value investing generates a non-zero expected excess return.” Then we turn to the data, and we find that the value factor has indeed generated a non-zero expected excess return, albeit with a large degree of year-to-year variability.
Now here’s the important part. The data never lets us accept our alternative hypothesis. Rather, we can only reject or fail to reject our null hypothesis. That may seem like semantics, but it’s hugely important.
When someone says, “the value premium is statistically significant at a 95% confidence level,” what they’re really saying is, “there is a 5% chance that, assuming the null hypothesis is true, we could have seen this result due to randomness alone.”
What do we mean “by randomness alone?” Imagine flipping a fair coin 10 times and having heads come up 8 times. Now imagine that you told someone you flipped a coin 10 times and it came up heads on 8 flips. Would they believe that the coin was fair?
Sometimes, rare things happen.
A statistical test with 95% confidence means that there is a 5% chance that a rare thing just happened and that the null hypothesis remains true.
Note that we can never accept that the alternative hypothesis is true. We do not accept that value investing has a non-zero expected excess return. Rather there is simply a small enough probability that the results we saw were due to randomness that we’re willing to give it a shot.
We either reject the null hypothesis with some confidence or fail to reject it.
With this in mind, we propose a simple null hypothesis for 2018: the market is probably right.
Hubris Sells, Humility Survives
This might seem like a rather odd null hypothesis coming from a firm that actively manages investment strategies. After all, it is equivalent to, “the market is efficient.”
The reason we believe it is an important null hypothesis is because it requires significant humility. It requires our saying, “we believe there is an opportunity here, but we’re probably wrong” as our default position.
Consider, for a moment, the hubris required to say, “the market is wrong” when “the market” is made up of millions and millions of highly educated participants, many of whom have access a wealth of computing power for processing information.
Consider that every asset is always held by someone at some time. When you sell something, someone is buying it. When you buy something, someone is selling it. What do they know that you don’t?
Think back to all the times you’ve read an investment article that made you change your mind on an investment thesis. Or articles written by people you may consider to be smarter than you, or who have access to better data.
Then assume that those people are on the opposite side of whatever trade you’re making.
All too often we see that hubris sells in asset management. A portfolio manager with a strong conviction and a convincing, articulate argument can do wonders for AUM growth.
But that same hubris is the antithesis of the humility required to reflect and ask, “why am I the only one seeing this opportunity in the market? Why isn’t everyone doing this?” We cannot possibly know everything, and we believe that humility is required for a portfolio to survive all the unknowns we will face in the long run.
The Market Probably Isn’t Broken
By way of example, we’re going to pick on a recent article, titled The Three-Body Problem, by W. Ben Hunt, Ph.D., at Epsilon Theory.
Let us preface this by saying that we’re big fans of Ben’s writing and that we generally agree with the conclusion that Ben draws in the piece. It is the details upon which we disagree.
In the piece, Ben argues that extraordinary monetary policy has swamped the traditional “quality –> yield spread” relationship in government bonds. As an example, he points to the fact that 10-year Portuguese Government Bonds are now yielding less than 10-year U.S. Treasuries: 1.85% versus 2.43%. As a reminder, these are the same government bonds that were yielding some 14% back in 2012.
What in the world is going on? If yield implies quality, how can the U.S. possibly be “junkier” than Portugal? In fact, the same question can be asked for much of the rest of the developed world. Has the market lost its collective mind? Why in the world would anyone in Portugal buy these bonds when they could just buy U.S. Treasuries instead?
Or, should we assume the market is probably right and it is our understanding that is wrong?
Indeed, the problem here is in our understanding.
As it turns out, we cannot simply compare rates of different government bonds. Why? Consider what it really means when we say that a 10-year U.S. Treasury is yielding 2.43%. It means that if you buy that bond for $1, every year the government will give you $0.0243, until the bond matures in 10 years when it will return your $1.
Similarly, in Portugal, you can buy the bond for €1 and receive €0.0185 each year until maturity, when you’ll receive back your €1.
Have you spotted the problem? The denominators of the returns are totally different. Yes, it looks like both U.S. and Portuguese bonds are quoted in percentage yield, but the actual cash flow is in totally different currencies. For us to evaluate these two investments, we have to put them into the same currency.
Let’s put some numbers behind this example. To make things easier, we’re going to use 10-year zero-coupon bonds (which allows us to ignore the intermediate coupon cash-flows) and just use a broad Eurozone yield curve.
Here’s the data:
Here’s the question: as a Eurozone investor, why wouldn’t I just invest in U.S. Treasuries? Better yet, why don’t I sell short Eurozone bonds and buy Treasuries to capture the spread? Smells like arbitrage to us…
Let’s try that.
First, we will sell short €1 of our Eurozone bond. Remember that in 10 years, we’re going to owe back €1.1024 (€1 x 1.0098%10).
Unfortunately, we can’t buy a U.S. Treasury with euros: we need to convert to U.S. dollars. So, we go to the forex market exchange €1 for $1.195 (the current EURUSD exchange rate is 1.195).
We then go to the bond market and buy $1.195 worth of 10-year U.S. Treasury bonds.
Now here’s the rub. We live in the Eurozone. Our currency is euros. Our debt is in euros. But in 10 years, we’re going to get back U.S. dollars. We certainly don’t want to take any currency risk, right? After all, we’re just trying to capture the spread of interest rates here, not introduce FX risk.
Fortunately, we can lock in a future exchange rate by using Forward contracts. Today, the 10-year EURUSD forward rate is 2580 pips. Note that quoting convention here is that Forward Points = Forward Price – Spot Price. Thus, with a EURUSD spot price of 1.195, we can back out the forward rate as 1.195 + 2580 / 10,000 = 1.453.
So, after 10 years, we receive $1.5312 from our Treasury investment. Our forward contract allows us to convert the $1.5312 into €1.0538 ($1.5312 x €1 / $1.453).
Now remember that we owed €1.1024 for the money we initially borrowed. After we repay our debt, we actually end up with a net loss of €0.0486 or about -0.5% per year.
As it turns out, European investors are not being stupid. Once we convert everything into the same denominator – euros – the negative “spread” is completely eliminated. In fact, from a U.S. investors perspective, there is actually a positive premium earned by investing in Eurozone bonds.
It appears the quality –> yield relationship is alive and well when we adjust for the denominator.
Note: We should be clear that the result here was somewhat expected. Covered Interest Rate Parity tells us that investors should be indifferent to interest rates earned in different countries (technically, on bank deposits). The no-arbitrage condition defines the relationship between spot currency exchange rates, forward exchange rates, and current interest rates in both countries. The theory requires, however, assumptions that the interest rates are risk-free (no defaults), frictionless markets, infinite liquidity, and no counter-party risk in the forward contract.
In reality, these assumptions do not hold, and CIP can be violated. In fact, post 2008 it has been violated with great frequency. Wu, Tepper, and Verdelhan (2016) explore why these violations have occurred and John Cochrane provides a succinct and accessible summary on his blog, The Grump Economist.
If you haven’t heard of CIP, you’re likely familiar with CIP’s cousin, uncovered interest rate parity, though potentially not by name. The uncovered form avoids buying the currency forward but acknowledges that the forward exchange rate should be the market’s expectation for what the rate will be in the future. Thus, if markets are efficient, it should be impossible to place the trade, unhedged, and profit over the long run and we should be entirely indifferent to higher rates in one country and lower rates in another. Yet the empirical success of the carry trade flies squarely in the face of this notion.
Despite these real-world violations, both covered and uncovered interest rate parity remind us that we should be indifferent to rates earned in different countries. Thus, the spread of the rates cannot be a meaningful indicator of quality. Rather, if investors are looking for relative quality comparisons of sovereign debt, they’d be better off comparing cross-currency basis spreads (which will capture relative credit-worthiness, liquidity, and supply / demand factors) or USD-denominated credit default swaps.
Illusory superiority – or the above-average effect – is a documented cognitive bias where the majority of individuals will rate themselves as above average. While this bias may do little harm for society (net positive self-belief is probably a good thing in aggregate), it may cause disaster for individuals in a market where excess returns are, ultimately, zero-sum. Belief in excess of your ability makes you the sucker at the poker table.
A null hypothesis that the market is probably right is a good way of reminding ourselves that we should deeply scrutinize our evidence to the contrary.
In our example above, it means asking the simple question of “which is more likely: that monetary policy has completely distorted markets to the point where yield spreads are now meaningless indicators of relative quality, or that we just forgot to account for currency?”
That is not to say the market is never wrong. Rather, the null hypothesis serves as a reminder that we probably need an overwhelming amount of evidence to the contrary before we take action. And even then, we should remember that we can never accept the alternative hypothesis that the market is wrong, but only reject that the market is probably right with some degree of confidence. The humility to accept that our evidence may be nothing but a fortunate permutation of randomness allows us to adequately hedge our confidence and design a portfolio that is robust to our hubris.
A portfolio designed to survive another year.