The Valuation Myth
July 15, 2002

It is amazing to me how many gurus now recommend buying bonds and selling stock.   This presumes that they know how to value stocks.   At the heart of this claim is the assumption that stocks are very similar to bonds in that we can simply discount the income stream to present value. Instead of discounting coupons we can simply discount dividends. I will attempt to show some of the errors in this logic and in the process explain why I think bonds are more risky than stocks at this time.

In my opinion, the main difference between a bond and a stock is specificity of payments. In its simplest form a bond specifies the face amount of money the bond will pay on a specific maturity date. If interest rates are 6% for a given class of 10 year bonds, a zero coupon bond of that class will sell for $1000/ (1.06)¹⁰ or $558. If interest rates go from 6% to 8% one year later, that bond will sell for $1000/(1.08)⁹ or $500, no ifs ands or buts. Bond prices vary inversely with interest rates. Interest rates are at a 40 year low, the federal government has spent the surplus we had and is spending money they don’t have in order to stimulate the economy and win the war on terrorism. So, if they can’t spend us into good times, they’ll spend us into inflation, or stagflation. That sounds to me like a prescription for interest rates rising and bond prices falling. The longer the maturity you buy, the more you’ll lose.

Most bonds have coupons that they promise to pay at specified dates in the future. If the company does not pay the coupon rate or face amount at the specified date severe penalties are invoked under the bond indenture agreement which usually prevents the company from doing much of anything until the bond holders are paid in full. If that same company decides not to pay the dividend on its common stock no penalties are imposed on management. They can begin new capital budgeting projects, pay themselves bonuses, buy a new Lear jet for the CEO, whatever, and the stockholders can do nothing, except sell their shares.

Discounted Cash Flow

The present value of a coupon bond can be determined for any coupon bond by discounting each coupon and the face amount at the current interest, i, in the equation below. This is exactly how people value a bond in practice. If interest rates change, all one need do is substitute the current interest rate in the equation to determine its current value. Again, if one could forecast correctly what interest rates would be at some time in the future, one could determine exactly what that bond would sell for at that time.

Now, if we make two Herculean assumptions: 1, that D’s are the same thing as C’s, that is, dividends are the same as coupons, and 2, that people can estimate the value of the stock at some future date so they can discount it like it was the face value of a bond, then, we could value a stock as simply as we value a bond by discounting at some interest rate k. The problem is, dividends are not the same thing as coupons. As mentioned above, the company can increase them, decrease them, or not pay them at all and shareholders have no recourse whatsoever in a court of law. And of course, nobody knows what the stock price is going to be at some time in the future.

As if the formula above for determining the value of a stock weren’t bad enough, financial theory goes on to say, for companies that will have a growth in earnings this formula collapses (mathematically) to D₁ /(k-g), i.e., the dividend that you will receive next period discounted at the cost of capital. Oh yes, I forgot to mention, k is not a known interest rate published in some financial publication, it is a theoretical concept. Does anyone know how to calculate it? NO! But Bill Sharpe has made an effort to tackle this extremely difficult task and was awarded the Noble prize for his effort.

Bill says, if investors are single period, expected utility of terminal wealth maximizers, who make their decisions based solely on the expected average return and the standard deviation of that expected return, then the cost of capital is:

COC = Risk free rate + Beta (Expected return on the market – risk free rate)

Unfortunately, none of these assumptions hold in the real world. But that’s the best we can do at the present time. However, if these assumptions were true, then a company whose dividend next period would be $4 and whose COC was 12% and had a 5% growth rate would have their stock sell for $57.14. Wow. We would then know the value down to the penny. Well, not quite. The dividend discount model assumes that dividends grow at a constant rate for eternity. That’s right, I said eternity. Furthermore, the company pays out the same percentage of earnings as a dividend every year until eternity, and the rate of return on equity is constant for eternity. Right, none of these assumptions hold in the real world.

The P/E Ratio

In man’s never ending search for a simple solution to a complex problem, the price to earnings ratio can be derived from the constant growth dividend discount model.

Even without my earlier comments about the underlying assumptions of valuation models recent headlines about standard accounting procedures for calculating earnings should cause one to question the veracity of the P/E multiple. Earnings are the last thing on the income statement after all the creative accounting has taken place. Firms that are profitable try to hide earnings so they don’t have to pay taxes. Firms that are unprofitable try to inflate earnings to keep their price up. Why would anyone think that this ratio tells them anything worth knowing? I know, someone found a time in history when it worked. What about all the times it didn’t? The point is, it is woefully inadequate to be reliable. .

The St Petersburg Paradox

Now for the coup de grace. In the 1700’s Bernoulli asked his colleagues how much they would pay to play a game where he tossed a coin and paid them 1 ducat if it came up heads and doubled the amount on each subsequent head. In other words, 1, 2, 4, 8, 16 etc. If a tail came up the game was over. The expected value of this gamble was an infinite amount of money. For example, after 51 successive throws of heads one would win more than 1,000,000,000,000,000 ducats. Yet no one would pay that amount and most would sell their chance to play the game for less than 40 ducats.

The point is, risk averse human beings will not pay the expected value of an uncertain outcome like…a stock price. Therefore, even if the valuation models mentioned above for stocks actually worked, nobody would pay that price anyhow!

The best hope I’ve seen for a better way to value stocks is Andrew Lo’s paper titled "Bubble Rubble, Finance In trouble" at www.alphasimplex.com In my opinion valuation models are crude filters for valuing individual stocks under normal circumstances and at peaks and troughs in the market, it’s valuation shmaluation, emotions rule. When you are fearless and everything you read, see, and hear encourages you to bet the farm…sell. When the media is scaring you to death and, as Rothchild said, "there’s blood in the streets"… buy. Well, Wall Street looks pretty bloody to me.

Three years ago fund managers felt they had to invest all their cash in tech stocks in order to get their bonus for beating the index. Now that the NASDAQ is down 70% those same fund managers are sitting on cash. There is over a trillion dollars waiting to go into the market and someday, holding cash is going to make fund managers lose their bonus. Then, as stocks rise and interest rates rise those sitting on long term bonds will see their portfolio values decline. No doubt they will console themselves by saying, "I won’t lose if I don’t sell." Wrong!!! You may have lost out on the best buying opportunity for the rest of your life.

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