We introduce a value-based investment model as alternative to the Capital Asset Pricing Model (CAPM) used by business schools, investment banks, and portfolio managers today around the world. We believe that the Capital Asset Valuation Model (CAVM) is a common sense approach to modeling risk-return in a way consistent with Graham and Dodd. We call it a model with some hesitation, as we only use simple algebra and common-sense to arrive at a solution. But the final solution may not come to much surprise many value investors.

**Our Starting Point**

In CAPM, expected return is dependent on beta, or price volatility relative to the general market as well as the average risk-free rate. It is inconceivable to us how expected returns can be measured as a function of past historical performance and the risk-free rate, as both are outside of the investor’s control.

Our starting point for the new model is recognizing that volatility is not equivalent to risk. To the contrary, as Graham points out in the Intelligent Investor, volatility is simply an opportunity to buy wisely when prices fall.

Our model defines risk as the probability of capital loss associated with a particular investment decision. Defining risk as the probability of loss allows us to define key points in what will become the equation for CAVM. The two key points are:

1) The expected return will be greatest when the probability of loss is zero.

2) The expected return will be zero when the probability of loss is 100%.

**Derivation of CAVM Equation**

Mathematically, the two points above can be plotted in a x-y axis, where y is the expected return and x is the probability of loss (risk).

The max and min points on the plot can be incorporated into a linear relationship between expected return and risk, where as expected, investment returns will be a function of risk. This yields the following linear relationship:

Re = Rmax – (Rmax)*[risk]

Since risk has been defined as the probability of loss, then: risk = 1-p, where p is the probability of gain, or a gain confidence interval. The equation becomes:

Re = Rmax – (Rmax)*[1-p]

or

Re = Rmax*p

This simple equation makes sense. It tells us that the expected return on an investment will be the maximum possible return one can achieve on a particular idea multiplied by a confidence interval. We believe that confidence interval p is dependent on only two things:

1) The certainty to which the gap between value and price will close within the desired or expected time frame.

2) The certainty to which the value of the investment can be measured from the information available to us.

To add a time variable into our equation, we add variable T as one with inverse effect on the expected returns. Our equation becomes:

Re = Rmax*[p/T]

Value investors may also recognize that the maximum expected return Rmax occurs when the gap between intrinsic value and price is zero, such that:

Rmax = (IV-Price)/Price

Where IV is the estimated intrinsic value and price is the current price. This equation is zero when IV=Price, or when margin of safety (MOS) is zero.

We, as value investors, define margin of safety as:

MOS = 1-[Price/IV]

So that if price for an investment is for example $20, with an estimated IV of $30, the margin of safety would be 33%. This means that we as investors are paying 67 cents for every dollar of intrinsic value.

Combining the equations for Rmax and MOS provides us with an equation for Rmax solely dependent on MOS:

Rmax = MOS/(1-MOS)

So our equation for expected return becomes:

Re = [MOS/(1-MOS)] *[p/T]

We believe, as value investors, that this is the equation every investor should be using as an alternative to CAPM. In fact, we believe value investors unknowingly make such calculation when evaluating potential upside vs. downside for each of their investments. The equation is simple, and implies that the only things that matter when making investment decisions are: the margin of safety (MOS), one’s confidence that our calculations are correct (p), and the time it takes for the price-value gap to close (T).

**Thoughts on the Risk-Return Equation**

There are several interesting thoughts that arise from the equation we have derived. Some are outlined below.

– Contrary to CAPM, risk decreases the probability of returns. Maximum expected return is only achieved by completely eliminating risk.

– The maximum risk on an investment is obtained on 3 different ways: margin of safety is zero, confidence interval p is zero, and time is infinity. Therefore, minimum risk comes from having large margin of safety, high confidence interval, and realizing value in the shortest time possible.

– Equation supports Buffett’s idea to investment in businesses whose “cash flows are highly predictable”. A highly predictable business would imply the investor has a high confidence interval p, since the probability of properly establishing an appropriate intrinsic value is high.

– Equation is valid in any type of investment scenario, e.g. stocks, bonds, real estate, etc.

– Equation is undefined as MOS = 1, so a margin of safety of 100% is impossible in the investment world (cannot invest at 0 cents on the dollar).

– Risk is independent of sector and/or diversification strategy. E.g. 1000 holdings will have equal expected returns as 10 holdings as long as the average margin of safety and average confidence interval is identical (though transaction costs would increase in proportion with the number of holdings).

– Investors concentrating in situations with high confidence intervals p (e.g. Buffett) have the ability to make high returns at lower margin of safety than average investor Investors with low p need to invest with higher MOS to make up for the difference.

– Portfolio of investors with identical stocks purchased at identical prices may pose widely different risks. First, MOS estimates will vary between investors. Second, investors may have different confidence intervals p because some the uncertainties of intrinsic value estimation will vary among them.

– Lower MOS will shift return line downward, diminishing returns for investors at identical risks.

**Challenges**

– What confidence interval p corresponds to the average stock market investor? We believe that the average investor decision-making process on risk amounts to a coin flip, so we believe p = 50% is appropriate.

– Confidence interval p is a “fuzzy” parameter which requires skill to evaluate:

1) The certainty to which the gap between value and price will close within the desired or expected time frame.

2) The certainty to which the value of the investment can be measured from the information available.

The skill to deal with these certainties (or uncertainties) can widely vary among investors.

– Average S&P500 return of ~ 6% suggests average investor has historically purchased stocks with an average MOS of 10%.

**CAVM in Practice: The ValueHuntr Portfolio**

We calculate the average MOS for our portfolio both at cost and at the current market price. Our analysis indicates that MOS at purchase was 38%, and a current MOS of 29%.

From MOS, we can then obtain the maximum return possible for our portfolio. Assuming an average confidence interval p of 50%, we can then obtain the expected return of our portfolio.

At the time of our purchases, our portfolio had an expected annualized return of 43%. Our gains have since lowered the expected gains to roughly 26%.

**Afterthoughts on ValueHuntr Portfolio Analysis**

– Importance of MOS is evident on the risk-return graph above. Even at 80% risk, expected return is still 10%.

– Steep value lines possible due to our focus on small caps, where big discrepancies between IV and Price occur more often than in mid- and large caps.

– Our expected return has gone from 43% to 24% due to investment gains. Ideally, we would re-balance our portfolio to shift to curve upwards by selling stocks with low MOS and buying stocks with larger return prospects.

– We assume that our ability to evaluate the certainty of investment returns given the information we obtain for our various companies is at par with the average investor. Hence, p = 50% (ability to evaluate risk amounts to a coin flip).

Any questions or comments regarding CAVM are welcomed.

on May 7, 2009 at 1:34 pm |widemoatAbsolutely excellent. Very well presented and illustrated. Better submit it to a finance journal.

I’m curious about your assumptions for T. 1 year would be great–but few price/value discrepancies get resolved that quickly, without a catalyst. In the case of David Einhorn and Allied Capital, it was many years.

Any additional thoughts about picking a value for T?

on May 7, 2009 at 3:06 pm |ValueHuntrThanks Widemoat. T is a variable which we have no control over. I suggest coming up with a worst-case scenario T for each position and averaging them. Notice that if T is large, you would have to compensate with a greater MOS to get the same expected returns.

on May 12, 2009 at 3:36 am |History of ACF Fiorentina » Blog Archive » Mean and predicted response[…] Introducing the Capital Asset Valuation Model (CAVM) […]

on May 31, 2009 at 11:50 pm |Monthly Update: Valuehuntr Portfolio Gains 89% in May «[…] We select stocks which are undervalued and with a catalyst in place. However, as a group, our stocks are managed based on their price advances relative to intrinsic value using CAVM, a model we have developed as an alternative to the CAPM model used by analysts and professors today. CAVM allows us to account for risk by defining it as the probability of loss rather than as volatility.To read more about CAVM, see our explanation here […]

on June 26, 2009 at 8:21 am |Our Alternative to CAPM «[…] According to Edward Thorp, the fundamental problem in gambling is to find positive expectation betting opportunities. The analogous problem in investing is to find investments with excess risk-adjusted expected rates of return. This simple premise is what allowed us to develop the Capital Asset Value Model (CAVM), which we first explained on a previous post. […]