Investing for gain entails risk, right? The real question is how much to pay for the risk. Stated otherwise, how much of a discount should an investor require for the level of risk in an investment? Economists have given us all sorts of fancy models to determine fair pricing. Not one has been able to top the seminal work of Harry Markowitz, William Sharpe and Merton Miller with their

__Capital Asset Pricing Model__. The world has been so impressed with the CAP-M as it is fondly referenced in business schools the trio was awarded the Nobel Prize in economics.**Required Return on a Stock =**

**Risk Free Rate + Beta of Stock X the Market Risk Premium**

**and**

**Market Risk Premium = Expected Market Return - Risk Free Rate**

Economic models are no different than any other construct - it is only as strong at its weakest link. Thus I set about determining the weakest element in the application of the CAP-M in today’s investment environment.

__First, there is the so-called risk free asset__. What is a risk free asset anyway and where can we get one? It seems like a good idea in the current uncertain economic environment.

To be free of risk the investment would have to be free of default risk. While it is true that the U.S. government could default on its obligations, it appears to be highly unlikely given Congressional power to print new money at its discretion. Second investment in the riskless asset would to have a known outcome from the start, with the exact return known to the penny. The investor would need to be able to invest the cash flows received along the way to maturity at a known rate. In other words, there could be no reinvestment risks prior to maturity.

The only investments that meet these two requirements are a zero coupon bonds or U.S. treasury bills with maturities of one-year or less. Yields on STRIPS, which are engineered zero coupon bonds, offer yields in a range of 0.99% for a one-year maturity to 2.6% for a ten-year maturity. U.S. Treasury bills with a one-year maturity are currently yielding 0.11% - yes, that is one tenth of one percent.

Stopping here would be a mistake. There is then the issue of time frame. Investing in a company is typically not a short-term exercise. Thus the risk free asset must fall in-line with the expected duration of the investment - one year, five years, ten years. It amy be necessary to "build" a zero coupon yield. Even if no zero coupon bonds of the appropriate term are traded, we can estimate zero coupon rates for each period by using the rates on coupon bearing bonds. To do this, we start with the single period bond and set the rate on it as the zero coupon rate for that period. We then progressively can move up the maturity ladder, solving for the zero coupon rates for each subsequent period.

Some academics, such as Aswath Damoradian of New York University argue that it really only makes sense to derive a period-specific risk free rate under particular circumstances. For example, if the yield curve is downward sloping (short term rates are much higher than long term rates) or excessively upward sloping, with long term rates exceeding short term rates by more than 4%, there is a payoff to being year-specific. In market crises, for instance, it is not uncommon to see big differences (in either direction) between short term and long-term rates.

__Next up in the CAP-M is the beta of the stock__, which of is a number describing the relation of a stock return with those of the financial market as a whole. A positive beta means that the asset's returns generally follow the market's returns, in the sense that they both tend to be above their respective averages together, or both tend to be below their respective averages together. A negative beta means that the asset's returns generally move opposite the market's returns: one will tend to be above its average when the other is below its average.

Beta is the key to the CAP-M. An investor has the choice of investing in the risk free asset or in another “risky asset.” How much more return should the investor require in order to be adequately compensated for the risk undertaken? The Nobel Laureates answered that question by suggesting that the investor should receive a premium commensurate with the premium of the rest of the equity market - commensurate to the tune of the stock’s beta. For example, if a stock has a beta of 2.0, it moves in the same direction as the overall market but moves twice as much. Thus investors in the asset should receive twice the market premium equity.

Not all beta measures are calculated equal! Thus it is necessary to check the beta measure against common sense. If beta, which is by definition a historic or backward looking measure, does not appear to capture the current sense of the company’s situation some adjustment may be needed.

Then there is the

__expected return for the broader market__. Based on the historical ratio of total market cap over gross domestic product (currently at 84.9%), the stock market is likely to return 5.6% in 2012 from this level of valuation. This includes returns from dividends, which is approximately 2.0%. Historical equity market returns and the implied risk premiums are very poor predictors of both short-term movements in implied premiums or long-term returns on stocks. Thus, if predictive power is critical or if market neutrality is a pre-requisite, the current expected market return and implied equity risk premium is the best choice. For those more skeptical about markets, the choices are broader, with the average implied equity risk premium over a long time period having the strongest predictive power.In upcoming posts we will be looking at required returns on stocks using the Capital Asset Pricing Model and the implied fair price. If the foregoing discussion provides anything more than a head ache, it is the assurance that valuation is in itself risky business.

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