Saturday, December 9, 2006

The other vaulation method - EGM

There is another way to value stocks besides DCF that isn't too bad. I don't know what its name is but we can call it the explicit growth method (EGM).

It is fairly well based in reality. How do you make money on a stock? You buy it, hold it for some time and then sell it. The profit (or loss) is the dividends that you have collected plus the capital gains (or loss).

So lets assume that we have an initial valuation metric P/E. One could use any of them such as P/B or P/D P/CF etc.

Lets ignore dividends first off. If the stock grows at G for N years then the earnings will be E_0 * (1+G)^N. If the valuation P/E stays the same you will have obtained a anulaized return of G. That pretty easy. If the valuation changes then the price of the stock will be P=(P/E) * E_0 * (1+G)^N

Your anualized return will be R=[r^(1/N)*(1+G)] -1 where r is the ratio of the final valuation to the initial. Example. The stock grows earnings at 10% for 5 years. The P/E goes down from 20 to 15 so that r=0.75. That is a 4% return. If the vaulation went the other way from 15 to 20 it would be a 16.5% return. If the valuation stays the same it is a 10% return.

You also have to add in dividends. We want to assume that the dividend payout ratio stays the same so that the dividend grows with earnings. With no change in valuation this is simple. You just add the dividend yield (which stays constant) to the annualized return from capital gains. So for example if G=10% and the yeield Y=2% then the return is R=12%.

But what if the valuation changes? This now depends on when and how the valuation changes and whether or not you reinvest the dividends or whether you invest them somewhere else at some other rate (ie the discount rate). Lets assume a constant change in valuation (linear in time) and reinvested dividends. In this case the dividends help more in the beginning if the stock valuation rises and help more in the end if the valuation drops. Thus, dividends have been called a bear market protection device. If Altria groups has a 4% dividend yield and the P/E drops by 50% you may have lost in capital gains but are now getting a dividend yield of 8% as long as they keep the dividend at the same rate. Not bad.

I believe you can just take the geometric mean of 1+Y which means that the average number of shares that you gain each years is AY = Y* (1 + (1-r)/2)

So your annulized return R is (keeping first oder in yield)
1+ R = r^(1/n) * (1 + G + AY) with the adjusted yield, AY = Y* (1 + (1-r)/2)

Example r=0.75 as before, Y=0.02 G=0.1 you get R =0.06. A 6% gain is not bad for a stock that declines in P/E by 25%.

The trick is that you need to reinvest those dividens when it declines and not sell out low. ideally you want to benefit from all three things. Growth in earnings, growth in valuations and also reinvesting dividends.

Lets look at a plot. We are going to run a Monte Carlo simulation and make a random distribution of P/E expansion factor r. Lets assume this is log-normally distributed and has a mean of 1 and sigma(log)= 0.15. We want to generate the distribution of returns for the two cases when we have only growth and when we have growth and a dividend yield. We will assume in eaither case that the sum of growth and yield are equal. For example in the middle panel we have Y= 3% so that black is G=10% Y=3% and the red is for only growth G=13%. The lower panel is for a higher Y=6%. One can see that the mean return is the same. The effect of having a dividend yield is that it reduced the variance of return. However this reduction is not very large even for rather large yields of 6%. This is for 10 years periods. The variance reduction is even smaller for shorter periods where capital gains becomes more important. I think this makes the case fairly well that dividends don't really protect you much in bear markets. However it could well be the case that stock which pay a dividend will not fluctuate as much. That is probably true and so you should expect less variation in returns due to this. However you do much better in reducing volitility just by buying another few uncorrleated stocks. I don't think one should discriminate against non-dividend paying stocks. It seems that adding the dividend yield to the growth rate is a pretty good estimate of return as long as you expect the valuation to stay about the same.

One could argue that this isn't really a fundamental valuation method since you have just postponed the question of what the correct valuation should be. That is true and DCF is probably better in this way. However this method has its merits. It is actually better related to how one actually makes money in stocks. Your not going to hold a stock forever. Valuations are affected by demand as well as supply and demographics have an effect on valuations. This can be input into this model but not really in DCF (unless you raise the discount rate). It seems a better way of treating dividends. We have a long historical record of what the market has been willing to pay for earnings. The average P/E of the market is about 15. I would say that for most mature companies, the P/E should be somewhere in the range 10-20 depending on their profitability and other factors.