 # Equity - Reading 35 - Pages 56 to 57 (Expected Return)

On page 55, the point being made is that the expected return can be viewed as the sum of a) the required rate of return and b) a return from the convergence for price to underlying value.

If I understand this right, the required return is the return from the next best investment of similar risk (opportunity cost) and if the price reflects intrinsic value only the required return can be earned. If there is a mispricing between market price and intrinsic value there is an an opportunity to gain from the convergence of price to value as well.

Its followed by a short example with required return of 7.6% and an expected alpha of 12.4%, together these comprise the expected return of 20%.

In the following blue box example, they do not add the required return of 9.5% to the holding period return calculated (14.7%) yet the two examples appear identical.

Can someone explain what is going on with this example and how it relates to the concept of expected return being the sum of required return and expected alpha? It seems they are just calculating the expected holding period return.

I’m pretty confused.

Thanks for the help.

I think the examples are not purely comparable.

In case of first example the current price is less and it should be 71 according to an analyst. 20% can only be realized if dividends declared are at 7.6% (as per market consensus) of current price and through convergence the investor earns 12.4% thus effectively earning 20%. 71 can only be the target price in year 1 if the required rate of return is paid in dividends. Or else according to the investors expectations after 1 year the price assuming no dividends paid should be 63.16*1.2 = 75.79. And if the stock is fairly priced and no dividends are paid then the 1 year target price should be 63.16*1.076 = \$67.96

The example in the blue box states that the Analyst thinks that the 1 year target price is 32. If according to the required rate of return 9.5% MSFT pays \$2.68 as dividends and as per analyst’s forecast the price converges to 32 then the realized return would be

2.68/28.73 + (32-28.73)/28.73 = 9.5% + 13.2% = 22.7%

which he certainly isn’t expecting as according to the example he is hoping for dividend yield to be 1.5% and convergence return to be 13.2% effectively thus expecting 14.7%

Thanks for the response. I think I get it now.

What I was trying to do was apply the idea of expected holding period return being the sum of dividend yield + price appreciation and the idea of it also being a sum of required return plus convergence return to both of the these examples.

In the first case, I agree that the only way a return of 20% can be realized is if the required return of 7.6% is met purely through dividends declared leaving the convergrance return (and price appreciation) of 12.4% to cover the rest.

In the second case, I do not think the return on price convergence or alpha is 13.2% but only 5.2%. Looking at it one way, the dividend yield is 1.5% and price appreciation is 13.2%, but a portion of this price appreciation return is already included in the 9.5% required return. To be consistent with the alternative way of thinkîng, the expected return should be 9.5% + a convergence return or alpha. This alpha is the additional compensation for discovering the mispricing.

If the target price were 30.53, then a return of 9.5% would be achieved making the stock fairly valued at 28.27. However, the target price is 32, so the additional appreciation of 1.47 over the fair price accounts for the 5.2% convergence return or alpha which is added on to the required return.

Let me know if you agree with this. Thanks for your help.

I agree with you as Expected alpha = expected return - required return This equation 2a written on page 54 clearly differentiates between Expected alpha and Expected return. The analyst is expecting a return from convergence to 13.2% while the additional would be 5.2% which if realized would be abnormal. The expected return on price convergence is 13.2% but it is not alpha as it includes required rate of return (as per eq 2a) which must be subtracted and dividend yield must be added.