Monday, May 16, 2011

How Can You Tell When Beta Provides a Useful Estimate of Your Stock’s Cost of Capital?

CAPM is the centerpiece of all standard finance textbooks whether Investments or Corporate finance.   It provides a standard first pass for assessing the cost of equity capital, by representing the firm with a single number beta.  Beta measures how sensitive the stock’s returns are to the returns from the market as a whole, and technically rests upon the statistical measure referred to as covariance.  The other major inputs into the CAPM estimate are the current yield to maturity from the long term Treasury bond and the equity premium for the market as a whole.  As a result, it is beta that drives the difference among firms for the cost of equity capital under CAPM.
But how can you tell whether this simplistic representation of a firm provides a realistic estimate or not? 
One way is to contrast this with a relative market based technique such as MCPM.  This is an option based method that exploits two important inputs into the problem at a firm specific level:  the yield to maturity on a company’s corporate debt and the volatility of the stock’s return.  First, the yield to maturity from debt exploits relative valuation.  A stock is riskier than it’s corporate bonds and thus the cost of equity capital should be higher than the cost of debt capital.  Second, the volatility of a stock’s returns determines the cost of insuring a stock using a put option, to ensure the returns from a stock are at least as big as the returns from it’s bonds.  Combined, MCPM exploits these two properties to establish a realistic estimate for the cost of equity capital. 
Thus technically CAPM extracts information from the covariance of the stock’s returns whereas MCPM extracts information from the volatility of a stock’s returns as well as the company’s credit rating.
In this blog we will explore how these ideas currently apply to Ford (F) and Wal-Mart (WMT).
What is F and WMT’s Stock Beta?

Beta provides a measure of the sensitivity of stock returns to the general market returns.  Thus, intuitively we would expect Ford (F) to be more sensitive to the general economy than Wal-Mart (WMT).  As a result, Ford should have a higher stock beta than Wal-Mart.  A quick check of some popular financial sites such as MSN Money and Yahoo provide strong support for this intuition.
Yahoo’s estimated beta (May 12, 2011) for Ford (F) equals 2.4 and for Wal-Mart (WMT) equals 0.36.
MSN’s estimated beta (May 12, 2011) for Ford (F) equals 2.38 and for Wal-Mart (WMT) equals 0.32.
Taking the mean provides F equals 2.39 and WMT equals 0.34.
You can also estimate your own beta and in the “how to” companion blog we show you how to conduct the entire analysis provided in this blog using the Valuation Tutor software combined with data available on the web.
What is the Volatility of Returns?
We can estimate the volatility of a stock’s returns in various ways including implied volatilities from option prices, as well as statistical estimates from past returns.  Beta is typically measured from the last 5-years of monthly returns relative to a broad based index such as the S&P500 index.  Thus for initial consistency we will first assess the volatility of returns from the current 60-months of monthly returns.  We will then re-estimate volatilities using the forward looking estimate implied from current long term option prices.
Again, Yahoo Finance and MSN Money provide the relevant data for this analysis in the form of historical price data that an investor can download and compute the volatility of returns from.
Using the last 5-years of returns our estimate for Ford is 78.3% annualized but the current implied volatility from an at-the-money leap on Ford is 25% (again in a companion blog we will illustrate how to compute the implied volatilities using the Valuation Tutor software).  A big difference but the latter estimate is current and more realistic for F today given the historic estimate covered the crisis period.
Conducting the same analysis for WMT results in 16.3% annualized from historical returns and 13.24% resulting from the implied volatility from long term options on WMT.
Question:  What is the cost of equity capital for Ford and Wal-Mart when estimated from CAPM?
Intuitively we expect that Ford has a higher cost of equity capital than does Wal-Mart because Ford’s business model results in greater operational and financing risk than Wal-Mart.  That is, automobile production is more capital intensive and sales are more sensitive to economic downturns and recovery than is food and general household goods.   This difference was dramatically illustrated during the economic crisis.  Both the above beta and volatility assessments support that Ford’s cost of equity capital is higher than Wal-Mart.  But how much higher and at what level?
There are three inputs into CAPM --- beta, risk free rate and the equity premium e.g., see
Input 1 Beta:
As developed above these inputs are:  F = 2.39 and WMT = 0.34.
Input 2 Risk Free Rate
The current 30-year Treasury rate is available at:
This site provides the bootstrapped zero Treasury curve under various compounding conventions. We will use the annualized rate which equals 4.88%
Input 3 Equity Premium
Pablo Femandez provides a rich source of information about equity premium estimates for a large number of countries including the US.  In his latest survey with Market Risk Premium Used in 56 Countries in 2011: A Survey with 6,014 Answers Pablo Fernandez, University of Navarra - IESE Business School, Javier Aguirreamalloa IESE Business School and Luis Corres Avendaño, IESE, April 25, 2011, they report that the median equity premium estimate for the US is 5.0% based upon a sample of 1503 respondents.
Combined, we can apply CAPM to estimate the cost of equity capital to be the following:
Ford = 0.1683 or 16.83%
Wal-Mart = 0.0658 or 6.58%
Question:  How do we know whether this is realistic or not? 
For example, if beta is zero then CAPM has the unrealistic implication that a company’s cost of equity capital equals the risk free rate.  Corporate controllers would love this but would face a tough battle trying to convince investors in the marketplace!   This has led to criticism of CAPM’s prediction for the cost of equity capital and alternative approaches suggested.  In particular, a relative market based approach provides a realistic check and balance.
The relative market based approach is an option based approach referred to as the MCPM suggested by James J. McNulty, Tony D. Yeh, William S. Shulze, and Michael H. Lubatkin,  Harvard Business Review, October 2002.  This option based technique referred to as the Market Derived Pricing Model and it’s implementation is summarized in:
The advantage of this approach is that it assesses the cost of equity capital relative to corporate bond rates.  Currently the 30-year AAA corporate rate is around 4.96% and BBB is 5.79% as reported by the Federal Reserve Bank.  For the case of Ford, it’s corporate credit rating has been steadily improving since the financial crisis whereas Wal-Mart’s has remained the strongest credit rating among major US retailers (around “AA”).  Ford’s corporate Fitch rating is around BB which is just below investment grade and this implies a corporate bond yield that is around 7.6% and for WMT around 5.24%.
Inputs for Applying the MCPM Estimate
There are five basic inputs required to apply MCPM.
·         underlying asset price= current market price of the stock
·         strike price =  forward break-even price (a derived number)
·         time to maturity = investment horizon
·         volatility = stock’s annualized volatility
·         bond yield = corporate debt rate for the time to maturity given the company’s credit rating
·         dividend yield= dividend yield on the stock

Briefly the premium over the corporate debt rate is calculated from the cost of insuring the stock with a put option such that it provides at least the same yield to maturity as the corporate bond.  This captures the simple idea that the cost of equity capital is bound from below by the cost of debt capital for a particular stock. 
Additional Inputs required from MCPM for F and WMT:
YTM:  F = 7.6%, WMT = 5.24%
Time to Maturity 30-years
Underlying stock price: F = $15.26, WMT = $55.72
Dividend Yield:  F = 0, WMT = 2.4%
Volatility:  F = 25%, WMT 13.24% (Historical Volatilities = 78.3% for F, 16.3% for WMT)
Forward B/E Point --- we compute this from the Valuation Tutor calculator
To compute the MCPM’s estimate for F and WMT we will apply the Valuation Tutor calculator as depicted below.  This software automatically computes the forward break-even price and the cost of the embedded put option. 
First, using historical volatilities:

That the two estimates are similar but the MCPM estimate is a little lower at 0.152 than is CAPM at 0.168.  However, if we use current implied volatility estimates from the LEAPS (long term options) on Ford then implied volatility is substantially lower at 0.25.  This reduces the MCPM cost of equity capital:

This estimate is significantly lower than the CAPM estimate of 0.168 which suggests that the historical beta is too high.  We can compute an implied beta for Ford by equating CAPM to MCPM which implies 1.31 not 2.39.
Implied Beta:  In the above we re-estimated beta for F using MCPM which provides a forward looking estimate for beta using implied volatilities from long term option prices.  But next consider WMT:
The following screen reveals that using historical volatilities for Wal-Mart the estimated MCPM cost of equity capital is 6.33% compared to CAPM’s estimate of 

Further if we use the implied volatility our refined estimate for WMT is:

And our implied beta for WMT is approximately 0.25 even lower than the estimate provided from the historical data but recall the historical data period covered the economic crisis of 2008/2009.
For Wal-Mart the estimates for cost of equity capital are pretty tight between CAPM and MCPM (6.58% versus 6.137%) and so this range is reasonable.  However, for the case of Ford CAPM appears to provide an unrealistically high estimate of 16.83% versus the MCPM estimate of 11.43%.  The latter would appear to be more reasonable for F today than 16.83%.
In a companion blog we will step through how to perform this analysis for your own stocks.


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