Ever since we posted our view on emergency funds, we have been thinking about a succinct, straightforward but also scientific way to debunk that bad, bad, bad advice that investors should hold large amounts of cash in a money market account. Here’s one try:
There is nothing wrong with reducing risk as a response to facing a future cash flow uncertainty. We personally don’t feel that urge right now because we currently have enough income flowing in to counter such unpleasant surprises. But not everybody has that luxury. People with high risk aversion, whether it’s because of cash flow risk or just general uneasiness about equity volatility, should certainly reduce their portfolio risk level. But it’s very likely they shouldn’t do so by holding large amounts of cash in a money market account.
It all comes down to the efficient frontier analysis. This frontier is efficient in the sense that for any point on this line there exists no lower risk portfolio with the same expected return, see the dark blue line in the chart below:
If you find yourself on the efficient frontier past the tangency point (see above), one can easily show that reducing risk involves no cash holdings, but rather keeping all of your portfolio in risky assets. Specifically, you simply move along the efficient frontier and into other risky assets with lower risk and more diversification, e.g. bonds.
Mixing in cash (earning the money market interest) would mean we move along the red connecting line between the money market return point (zero risk, very low return) and the initial portfolio. But by definition, this line cuts into the interior of the efficient frontier. You reduce expected return by more than you have to. If instead you walk along the efficient frontier you can reach the same expected risk level but with a higher expected return (or alternatively the same expected return but lower risk) than the portfolio with emergency cash. Of course, you still give up some expected return, that’s the opportunity cost of lower risk, but at least you avoid the efficiency loss of the money market fund.
Example:
In the numerical example, see table above, our investor is no longer comfortable with a 100% equity portfolio. Instead of keeping 20% in cash, thereby reducing expected risk to 12%, the investor could move into 10y government bonds with a higher return than cash and even a little bit of negative correlation with equities. You can reduce the equity share by just under 20% and still maintain the 12% risk target. The expected return is about 0.30% higher than under the cash scenario. 0.30% is not trivial when we consider that this is simply from reshuffling 20% of the portfolio!
Conclusion:
For the defender of the emergency fund, if the argument has to do with risk mitigation we agree that an (almost) all equity portfolio like ours might too risky. But holding large amounts of cash is not the right solution either. Investors should move along the efficient frontier, not to the interior of the efficient frontier!
Some Caveats:
- This doesn’t apply when you’re not past the tangency portfolio. But few people are. With enough diversifying assets the tangency portfolio has a very low expected return and low risk and we can almost be guaranteed that most investors are beyond the tangency point. In the numerical example above the tangency point has about 60% bonds, 40% stocks, generating 3.7% expected return, much less than most people target. With more assets in the mix this could be even lower (shifting the frontier to the left and the tangency point in a southwestern direction).
- All of this analysis doesn’t apply if you are already willing and able to take the tangency portfolio and scale it up through leverage, thereby effectively shorting cash. See our post here on why you want to do that. In that case, you certainly don’t want to hold cash in an emergency fund. You would merely short less cash if you want to reduce risk. The same result holds but the analysis is sightly different.