## Sunday, February 15, 2009

### Alternatives to Regression Betas

In my prior post, I explain why I am averse to regression betas - the high standard errors of the estimates, the backward-looking nature of the estimates and the loss of intuitive feel for risk. In this post, I would like to look at alternatives that are offered to regression betas, with an eye towards making better estimates:

1. Relative standard deviations: The beta is a function of the standard deviation of the stock, the standard deviation of the market and the correlation of the stock with the market:
Beta = (Correlation between stock and market) (Std dev of stock)/Std dev of mkt
The primary culprit behind the high standard error of betas is the shifting correlation number. Hence, there are some who suggest using an alternative measure of relative risk:
Relative Std dev = (Std dev of stock)/Average std dev across all stocks
Note that the denominator has to the average standard deviation across all stocks, not the standard deviation for the market, since you want the relative risk number to average out to one across all stocks (and it will not if you use the standard deviation of the market).
Pros: This number, like beta, should average out to one across stocks and should have lower standard error; even in a period like the last quarter, the standard deviations rose across the board and the relative standard deviation was fairly stable.
Cons: You are looking at total risk (not just market risk), which may not be appropriate for a diversified investor. You are also still backward looking and dependent on stock prices.

2. Option based approaches: A few years ago, there was a hue an a cry, arising from a paper published in the Harvard Business Review, which claimed to have come up with a forward looking estimate for risk. In the approach, the implied standard deviation of stocks is backed out of traded options issued by the company and compared to the standard deviation of bonds issued by the same company.
Cost of equity = Cost of debt *(Imp std dev of equity/ Std dev of bonds)
Pros: Forward looking, becauase you use option prices to back out standard deviation.
Cons: Works only for companies that have traded options and bonds... and it mixes up total risk and market risk. Does not strike me as a general approach that will work with most companies.

3. Accounting betas: Rather than regressing stock returns against market returns, we could regress changes in accounting earnings at a company against changes in accounting earnings for the entire market, and the slope would be the accounting beta.
Pros: Not dependent upon stock prices and can be estimated even for private businesses. For those who do not trust markets, accounting earnings offer a more stable alternative (assuming that you trust accountants).
Cons: Accounting earnings are often smoothed out and lag true earnings. Furthermore, the number of observations in your regression is restricted. With quarterly statements, you will have 20 observations over 5 years and the resulting standard error will be huge.

4. Bottom-up Betas: In this approach, we start with the businesses that a firm operates in, estimate the betas of these businesses (by looking at the average regression betas of publicly traded firms in each of the businesses) and clean up for differences in financial leverage.
Pros: The average across many regression betas will be more precise than any individual company's regression beta. It can be computed based upon the current or even a future business mix of a company and for private businesses.
Cons: You do need to find publicly traded companies that operate predominantly or only in each individual business and you the average regression beta does reflect the past. For instance, the average beta across all banks over the last 5 years may understate the true beta for banks for the future.

I am a firm believer in the last approach. Since there are lots of mechanical details that can trip you up, I do have a link on my site where I examine these:
More in my next post!

Mahesh Sethuraman said...

Hi,

I have a doubt about the option based approach for calculating Cost of Equity. Even Option writers calculate volatility (Garch, Arch, EWMA etc..)based on which they price the option right and that in turn is backward looking isn't it? And implied vol is nothing but the same extracted from price (agreed it varies everytime the option is traded). But theoritically the Cost of Equity calculated out of this should still be backward looking isn't it?

Infact I wonder if I could argue this logic backwards too. Assuming that stock prices are efficient, then I can extract the Cost of Equity from the market price of a stock and use that to find out the volatility that I need to plug in for calculating my option price. I am not sure if I am making sense???
My primary doubt is does this method assume that option markets are more efficient than equity markets?

eran said...

Dear Prof. The only thing that "bugs" me about the bottom up beta method is the debt beta. Then again, I wouldn't want to waste a lot of time calculating it. Is it safe for me to assume a common 0.2 debt beta for all companies including the one I'm valuing?

eran said...

I'm sorry, Valuating. A second note: if the debt beta is assumed to be zero, the cost of debt should be equal to the risk free rate, isn't it?

Aswath Damodaran said...

If the debt beta is zero, we are assuming that there is no market risk in debt. In other words, if default risk is uncorrelated with the rest of equity risk, debt can have a zero beta and still have a cost higher than the riskfree rate.

Tanmay said...

Hi Mahesh,
You can calculate the option price in whatever way you want , but the implied vol is what the market tells you (the market may not believe in whatever models you might use).

Hi Prof, i have a more technical question here..unless you stick to a model (say BS for example), the IV is model dependent; if you want to get a model free IV, it is under the risk neutral probability, so your option implied beta is some sort of RN option beta. Is that very helpful beta?

Mahesh Sethuraman said...

Hi Tanmay,
I just quoted the models to show off that I know them!!! (Actually to emphasize that there must have been some method used by the option seller).
I understand that Implied Vol is a result of demand and supply and may not even have anything to do with the models. My only question was that whether we use any model or not, how's the implied vol going to be forward looking? Isn’t just the market view of expected future vol just like the traded equity price is the market view of all the future cash flows of the company discounted back at CoC?

Tanmay said...

Hi Mahesh,
Let me try to explain more clearly. For a moment forget how options might be priced. Options are contracts that will result in certain payoffs, if stocks end up more or less than some value in the future. So to get a value of that option, you need an assessment of how a stock might end up on an expiry day of the option, or in other words you need a probability distribution of the stock on the day of expiry. Suppose this probability distribution is normal, it can be characterized by some mean and variance. Now if i give you the option price, you can back out some information about the distribution (=> some info about the variance). Now, hypothetically, you can think that you have options available for expiry for each day which means that you will have information on everyday's variance. So collectively you can have information about the accumulated variance (added upto all days till expiry). This is what is implied volatility is in a loose sense.
You should note that you are given the price of the option independently (it has nothing to do with any formula).

Aswath Damodaran said...

If your argument is that implied volatility can be wrong because option option markets are inefficient, I can live with that. However, just as the only variable driving bond prices is default risk, the only unknown in option pricing is the volatility. Unlike equity investors, who can get distracted by multiple inputs that they have to estimate, option traders just have to get the volatility right. Hopefully, they do a reasonable job of it. But as I noted in my post, even if they do, I don't think that equity risk should be based on implied volatilities.

Mahesh Sethuraman said...

ya precisely, That's my argument. I guess I didn't put that question across very well. Thanks for the clarification.

editor said...

Hi, I agree with your suggestion of using bottom up betas, but still...they don't really solve the problems of using regression betas, do they? As you mention in your post "In my prior post, I explain why I am averse to regression betas - the high standard errors of the estimates, the backward-looking nature of the estimates and the loss of intuitive feel for risk.".
Since you need to use regression betas of other businesses, standard errors of those are still high; they are still backward looking by nature and OK, they may help a bit with the last part. Am I missing something here?

Best regards,
Bojan

Ravi said...

Further to what 'editor' commented, while bottoms-up beta addresses the problem of reducing standard errors of estimates, does it not end up using the beta of a basket of fruit when you are valuing an apple ?

In other words, while the differences in financial leverage between the company being valued and the industry is factored in when determining the company's beta (and you could perhaps factor in operating leverage too), how does one factor in basic business differences (in product, branding, sales & distribution strength, risk-taking, new lines of business, stage of growth, rate of growth etc). Would these not be substantial ?

Andreas said...

The Beta of an ATM put option on a stock

a. is always negative.
b. could not be negative.
c. could be positive.
d. is equal to the Beta of a call.

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