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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.

graham_quote

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).

 plot1

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.

 plot31

 

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.

 plot2

 
– 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%.

 mos11

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.

 rmax1

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%.

 cavm-plot1

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.

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Today we examine the Capital Asset Pricing Model, which value investors tend to be skeptical of.

The CAPM assumes that the risk-return profile of a portfolio can be optimized. According to the theory, an optimal portfolio is one which displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Furthermore, because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta. When the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio (see Figure below).

 capm

According to CAPM, beta is the only relevant measure of a stock’s risk. It measures a stock’s relative volatility – that is, it shows how much the price of a particular stock varies relative with how much the stock market as a whole moves. If a share price moves exactly in line with the market, then the stock’s beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15% if the market fell by 10%.

A small and reprobate minority, value investors in the Graham-and-Dodd mould understand the shortcomings of the theory, and disregard both the conventional definition of investment risk and the standard practice of investment risk management.

 

Shortcomings of CAPM

There are two problems we see with the conventional risk-return relationship proposed by CAPM.

The first one is that the expected market rate of return is usually estimated by measuring the geometric average of the historical returns on a market portfolio (i.e. S&P 500). CAPM assumes that expected market return always follows past performance, which is a dubious assumption (as shown in the housing bubble burst of 2008).

The second problem is that the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return. In a similar fashion as the expected return, the average risk-free rate is somehow dependent on past performance, which is not a sensible assumption to make.

Several other assumptions are:

a) The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

b) The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors’ preferences more adequately.

c) The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).

d) The model assumes that the probability beliefs of investors match the true distribution of returns. A different possibility is that investors’ expectations are biased, causing market prices to be inefficient.

e) The model assumes just two dates, so that there is no opportunity to consume and rebalance portfolios repeatedly over time.

 ValueHuntr Portfolio According to CAPM

We have used CAPM to measure the expected performance of our ValueHuntr Portfolio. The analysis, as shown in the figure below, indicates that our portfolio is one with high risk. CAPM estimates our expected return at nearly 5% due to a volatility of 10% above the market average beta of 1.

 capm_valuehuntr

Obviously, we believe these results do not accurately reflect the prospects of our portfolio, as the volatility of our holdings tells us nothing about risk. Tomorrow, we will introduce a simple relation developed by ValueHuntr to be used as an alternative to CAPM.

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