Which stocks to buy? I don’t know, but buying all of them is better.

Update: The ft reported that the bonds futures market had priced in the possibility of a Fed exit from QE, which will increase Treasury Yields (and also make stocks expensive). Common sense dictates that the programme will be executed gradually, but perhaps it is time to focus on fundamentals. Too much noise have been made.

An economics professor once asked me what was the worst question I had been asked about as an economics major. I told her it was “Where do you think the stock market is heading?”

With the S&P 500 climbing to its historic heights, surely there are winning stocks that we can all cash into? Maybe the rally of the S&P 500 is driven by fundamental changes in the economy? Conceivable, but I wouldn’t put my lunch money on that bet.

Two New York Fed economists,Fernando Duarte and Carlo Rosa have recently surveyed models and market risk premium estimators used by practitioners in investment management to assess whether stock prices are cheap. By cheap, we mean that the expected return of a stock at this point in time is high. (If you are confused, consider this. If you can buy a stock today at $1, and it will sell for 1.18 tomorrow, you will have made an 18% return on your investment when you sell tomorrow. So expected returns “scales” your investment up.)

So what are the driving factors that describes the expected returns of a stock? That depends on the asset pricing model that is used to price the stock (some can be parametric, while some can be semi-parametric). The CAPM is one of the most widely used model, and it says:

Expected Return= risk free interest rate + Beta*(Market Risk Premium)
The Market Risk Premium is simply the return of the market minus the risk free interest rate. Some of you might realise this is in fact a univariate regression, and you are right. Which also means that upon further contemplation, we should rightly suspect that the CAPM Beta suffers from omitted variable bias in practice. Personally, I’d at least try to use a multifactor model, which is basically a higher dimension of CAPM that prices other dimensions of risk as a habit of having sound econometrics put in place. I went of a tangent in this paragraph, so let me circle back to my main point.

The following graph is the weighted average of risk-premiums backed out from the models and survey conducted by Duarte and Rosa. The duo argues that the equity risk premium has reached a historic high, which suggests that stocks are cheap today.


Moreover, they argue that the higher risk premium manifests itself in a 5-year time horizon.


In a similar vein, Greg Mankiw provided excellent bite-sized summaries of research on stock market returns in a New York Times column. I’d like to note that while many may agree that “holding stocks is a good bet,” it’s far from being a consensus view in academia. In fact, using forward-looking measures, Prof Lubos Pastor believes that stocks are riskier on the long-run. Paper downloadable here.

What is noteworthy is that the Fed Reserve Economists also argued that the equity risk premium is high because of low treasury yields. In their words,

“The figure makes clear that exceptionally low yields are more than enough to justify a risk premium that is highly elevated by historical standards.”


So what do we make of all of these? It does seem like an unintended consequence of low treasury yields is to make stocks cheap and bonds expensive. For now, a heavier tilt towards stocks would be better. Moreover, allocation of bonds should tilt towards bonds in countries with no zero interest rate policies, although always bear in mind that attractive returns means higher risks!

Interestingly, Prof Mankiw says he tilts slightly more towards stocks, with 60% of his wealth allocated to that asset class. His lower exposure to bonds makes sense, as a tenured professor his human capital is essentially a risk-free (Harvard has high credit worth right?) annuity granted by Harvard. (Inside joke:McGill is the Harvard of Canada,but we are heavily in debt. She’s right? )

Now to justify my qualification that “buying all of them is probably better.” Instead of investing in individual stocks, there are index funds that allows you to purchase a basket of stocks that are grouped by themes. For instance, you can own fractions of the stocks that make up the S&P 500, with the result being that you get to diversify away some of your risks. The risks that gets “washed away” are firm and industry specific risks (so that if Apple’s share price drops, or GM,Chrysler and Ford run into trouble again), your entire portfolio won’t be too adversely affected. However, keep in mind that not all risks can be diversified. If it is a risk most people care about, if you are averse to it it will cost you a lot; if you are willing to assume it the market will compensate you heavily for it.

Finally, I’d like to caution against asking for advice of “which stocks to invest?” Yes, we’d all like to cash in on a winning stock, but keep in mind that not all of us are the same. Some of us have “deep-pockets” and could assume risks that people are averse to, and as a result is able to stomach the risky, but potentially lucrative returns in the market. And clearly we cannot all share the same view that a particular stock is a winning stock, someone else has to hold the opposite belief to enable them to want to sell it to you.


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