PER and Risk Aversion

We will give an example to make it clear. The XYZ Company obtains some annual benefits of 100 million dollars and it is hoped that these do not change in the future. There are 10 million shares; therefore, the profit per share (EPS) is of 10 dollars per share. How much is the share of XYZ worth? Well, this depends on whom it’s for. If the investor Mr. Smith is very adverse to risk, he will only get in when he expects to obtain an elevated profit, for example, 20 for 100. Therefore, he will be willing to pay 10/0,20 = 50 dollars for the XYZ share. On the other hand, the investor Mr. Chadwick is less adverse to risk and sees that the interest rates are at, for example, 8 for 100 and with a 15 for 100 obtained in shares he would already be content. Therefore, the investor Mr. Chadwick would be willing to pay 10/0,15 = 66 dollars for the XYZ share.

Let us suppose that the interest rates go down from 8 for 100 to 3 for 100. Both investors will reduce their expectations of profit. Mr. Smith who used to enjoy his 8 for 100 in fixed rate now sees that he is barely obtaining the 3 for 100. He is probably willing to enter in shares even if it is gaining only the 12 for 100 instead of 20 for 100 that he had asked for before. At the same time, the investor Mr. Chadwick will reduce his expectations of profit, for example, from 15 for 100 to 10 for 100. This automatically makes the investors, Mr. Smith and Mr. Chadwick to be willing to pay 66 and 100 dollars respectively now, for the share of XYZ instead of the 50 and 55 they paid before. The conclusion of this is that the downfall of the interest rates have changed the value of the share for both of them, and they are now willing to pay more for it.

To sum it up, the price of the share depends on the profit the investor desires to obtain. Assuming that the profit per share is constant, if the investor wants to obtain high profit, he will want to pay a little bit for the share. The profit asked for by the investor depends on two factors:

• Risk free profit, in other words, the level of the interest rates.

• The risk premium the investor solicits in function of his lesser or greater risk aversion.

In other words we say that K = risk free + risk premium; the profit solicited by the investor is equal to the risk free interest plus the risk premium.

PER and Interest Rates. To sum it up
The Price Earnings Ratio of a share, or of all the market shares represented by an index, go up and down in function of:

• Movements in the interest rates. This is what has occurred in Spain and in the European markets in the last years, due to the decrease of the inflation and the implementation of the euro.

• Movements in the risk premium. All of a sudden there are two or three pieces of news or information that make people become fearful, which makes us increase the risk premium that we ask from the share and this causes the price that we are willing to pay to go down immediately. This is what happens every time a crisis is unveiled or rumors of one spreads around. One such example of a crisis was the summer of 1998. Or to the contrary, if there is a feeling that every thing is going well and everything is wonderful, the investors resume their aversion towards risk – their risk premium – and therefore, they ask for less profit and the prices go up.