May 11, 2010

# Market Volatility Has Doubled: What’s in Your Portfolio?—A Commentary by Ian Ayres ’86

*The following commentary was posted on newyorktimes.com on May 11, 2010*.

**Market Volatility Has Doubled: What’s in Your Portfolio?**

By Ian Ayres ’86

Jim Cramer made an interesting point on CNBC during the market meltdown last Thursday. Host Erin Burnett asked Cramer to explain the graph of the tanking Procter & Gamble price, and Cramer responded:

That is not a real price. Just go buy Procter & Gamble. When I looked at it, it was at 61, I’m not that interested in it. It’s at 47? Well, that’s a different security entirely.

In an odd way, Cramer’s impulse to buy more of P&G after a price drop resonates with the much more cautious analysis of Robert Shiller. Shiller has counseled paying attention to the CAPE, the cyclically adjusted PE ratio (also known as the PE10 because it’s based on 10 years of trailing earnings). When the CAPE is high (greater than 20), one might expect lower future stock returns. When the CAPE is low (greater than 10), one might expect higher future returns. Shiller has studiously avoided turning CAPE into an explicit investment rule. But followers of Shiller – CAPEd crusaders – have championed using the PE10 to time the market. Like Cramer, these Shiller acolytes would advise putting more in the market after the PE10 falls.

In Lifecycle Investing, Barry Nalebuff and I are agnostic about the viability of using the CAPE to time your exposure to stock market risk. On the one hand, theory (including the capital asset pricing model) suggests that you shouldn’t be able to profitably predict future stock price movements from the current PE ratio. On the other hand, Shiller and others have brought forward some persuasive evidence that the PE10 has been correlated with future returns.

But, in some ways, we’re even more attracted to adjusting your exposure to the stock market based on volatility. The CBOE’s volatility index, VIX, provides a readily available quantitative measure of just this – the market’s expectation of the future standard deviation in stock prices. (I wrote about the VIX before at the end of 2008, shortly after it had reached an apocalyptic 80 percent.)

When market volatility rises, investors should shift away from holding stock. It will come as no surprise that the VIX has skyrocketed in the last few days from its normal level (around 20 percent) to its Friday close of 40.95 percent. It’s amazing how well the VIX tracks my own state of unease. Before I checked my iPhone on Thursday evening, I was pretty sure the VIX would be above 30 percent.

(The elevated VIX through Friday provides some evidence that the market does not believe the “trader goof” story that the Thursday meltdown was caused by a trader mistakenly selling $16 billion instead of $16 million shares of P&G. There’s even some evidence that the VIX started moving before the S&P meltdown.)

From a market timing perspective, the meltdown on Thursday and Friday has two opposing effects. The drop in the PE10 would tend to make traders want to invest more in the market. The increase in the VIX would tend to make traders want to invest less in the market.

Which effect dominates?

A simple equation from our book (which is inspired by the seminal articles of Samuelson and especially Merton (equation 25)) suggests that the volatility effect is much larger.

The share of your retirement portfolio that you should invest in stock might be governed by this fairly simple equation (which can be found on p. 138 of Lifecycle Investing):

Samuelson share = Return/(Risk2 * Risk Aversion),

where “Return” is the expected equity premium on stock (the extent to which the stock returns are expected to exceed the government bond rate), “Risk” is the standard deviation measure of future stock return volatility, and “Risk Aversion” is a quantitative measure of your relative risk aversion.

This simple equation can help adjust your portfolio exposure to changes in both the PE10 and the VIX. Indeed, the current VIX number (available here) can simply be plugged into the equation as the market indication of risk. And using a simple regression (see an example here), it’s possible to take the PE10 (available here) and plug in a PE-contingent estimate for the expected equity premium.

In fact, Barry and I have created an excel file that is downloadable at our Lifecycle Investing webpage.

A month ago (when the PE10 was 21.7 and the VIX was a low 16.48 percent), our Samuelson share calculator would have advised someone with moderate risk aversion to invest 46.3 percent of his or her retirement portfolio in stock. But as of Friday’s close, with the fall of the PE10 to 20.15 and the dramatic increase of the VIX to 40.95 percent, our calculator would advise the same person to invest just 9.4 percent in stock.

Our book has been criticized for promoting overly aggressive stock advice. But what’s bold about our strategy is not the size of our Samuelson share; instead, it’s our estimate of the size of your retirement portfolio. You see, we think that many young people should do more than expose just their current savings to the stock market. We think they should also expose some of the present value of their future saving contributions. Here’s an example from our book (p. 22, part of a larger excerpt that you can read for free here):

If you are thirty, earning a steady $100,000 per year, and putting aside $5,000 then, mathematically, it is as if you have $120,000 invested in bonds. Your future savings contributions of $5,000 a year over the next thirty-six years are worth $120,000 today. Thus if you have $50,000 in current savings and 90 percent of that invested in stocks, it isn’t the case that you have 90 percent of your assets in stocks. A more accurate picture is that you have $45,000 in stocks and $125,000 in bonds ($5,000 from current savings plus $120,000 future savings). Only 26 percent of your true total savings portfolio is in stocks. Investing a little more in stocks when young isn’t as risky as you may have thought.

Actually, the percent in stock is far lower than 26 percent. If you earn $100,000, you can expect that Social Security will replace about 25 percent of your income upon retirement. That replacement income is even more valuable because it is indexed to inflation. To buy an annuity that provides the same terms would cost roughly $500,000 at the time of your retirement, or about $190,000 today. Thus your total bond holdings are closer to $315,000. That means your $45,000 in stocks is only 13 percent of your portfolio. Here you were thinking that 90 percent was a high percentage to put in the market. But when you think of how much of your wealth is already in bonds, even putting 200 percent in stocks only brings you up to 28 percent overall.

A month ago, we’d probably have advised this 30-year-old to invest on a leveraged basis to expose about half of the $170,000 of current (50k) and future (120k) savings to the market. But the logic of risk and return during these uncertain times counsels to back away from leverage for the moment. With $50,000 saved, our 30-year-old would have more than enough cash on hand to invest 9.4 percent of the present value of his or her current savings and future saving contributions. ($15,980 = 9.4%*$170,000.)

But a 25-year-old with a $200,000 present value of future saving contributions and only $5,000 saved would still do well to invest on a leveraged basis – even in these uncertain times. 9.4 percent of $200,000 is $18,800. Our book’s approach suggests that our hypothetical 25-year-old should invest in stock indexes on a 2:1 leveraged basis by borrowing $5,000 and exposing $10,000 to stock market risk. (If you wonder why we advise stopping at a 2:1 ratio, you can listen to Barry’s explanation in this video FAQ.)

The market rebounded yesterday on both fronts. The S&P jumped by more than 4% and the VIX was thankfully down to 28.84. But there are still two big take-away points here: 1) the optimal stock allocation percentage should be contingent on the expected amount of stock market risk; and 2) independent of the allocation percentage, it is important to think about the present value of your lifetime savings contributions when estimating the true size of your retirement portfolio. It’s prudent not to count your chickens before they hatch. But you should discount your chickens before they hatch. Young investors have a present value of future savings that is more than zero. Time diversification counsels them to expose some of that present value to the risks and rewards of stock ownership today.