# Expected return

Hi, all. Could anyone please give me a hand with the following.

Equity (p46) states that “investor’s expected rate of return has two components: the required return (earned on asset’s current market price) and a return from a convergence of price to value”. The next page gives the following:

E® ~ r (required return) + (Vo - Po)/Po.

Then question 13 on page 88 asks to calculate the expected holding period return at the time of purchase.

• Shares were purchased for \$20.75 per share
• At the time of purchase research suggested that shares were expected to sell for \$29 per share at the end of a 3 year holding period.
• At the time of purchase, the required rate of return (CAPM) was estimated to be 12.6% (annualized).
• Exactly 3 years after the purchase the shares were sold for \$30.05 per share.
• No dividends were paid over these 3 years.

Then the answer (p 92) calculates the expected holding period return as (Vo - Po)/Po = (\$29 -\$20.75 ) / \$20.75. I wonder why they do not account for required return.

Thanks.

If we are given an expected price we use this one to calculate expected return.

The formula you wrote E® ~ r (required return) + (Vo - Po)/Po says only that price will converge to its intrinsic value Vo and this will be one part of return. The other will be your required rate of return. There is no expected price in this formula.

Required return, realized return and expected return are different things and you should use different inputs to calculate each other, but imo they are pretty intuitive.