- CFA Exams
- 2023 Level I
- Topic 5. Equity Valuation
- Learning Module 21. Return Concepts
- Subject 1. Return Concepts

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##### Subject 1. Return Concepts PDF Download

**Holding Period Return**

It is the percentage by which the value of an investment has grown for a particular period. It is the sum of investment income and capital gains divided by the initial value.

_{n}= (Income + P

_{n}- P

_{0})/P

_{0}

**Realized and Expected Return**

If the investment is sold, then the realized return can be calculated. If not, then the investor can form an expectation concerning the investment income and final selling price, and thereby have an expected holding period return. The expected return is the average of probability distribution of possible returns. For example, if you knew a given investment had a 50% chance of earning a 10% return, a 25% chance of earning 20% and a 25% chance of earning -10%, the expected return would be equal to 7.5%: (0.5) (0.1) + (0.25) (0.2) + (0.25) (-0.1) = 0.075 = 7.5%.

Although this is what you expect the return to be, there is no guarantee that it will be the actual, realized return.

**Required Return**

It is the rate of return used by investors to decide whether an investment is attractive or not. It represents the opportunity cost for investing in the asset given the asset's riskiness. If the investor's expected return is higher (lower) than the required return, the asset will appear to be undervalued (overvalued).

Realized alpha = Actual holding period return - Contemporaneous required return

When an investor's intrinsic value estimate for an asset differs from its market price, the investor generally expects to earn the required return plus a return from the convergence of price to value. When the asset's intrinsic value equals price, however, the investors only expects to earn the required return.

**Discount Rate**

It is the rate required by investors for delaying consumption. The market required rate is typically used as the discount rate in finding the present values of expected future cash flows.

**Internal Rate of Return**

This is the discount rate that equates the present value of the asset's expected future cash flows to the asset's price. If we define cash flows as dividends and assume a stable dividend growth rate for the indefinite future, the intrinsic value of an asset is:

**Learning Outcome Statements**

CFA® 2023 Level I Curriculum, Volume 3, Module 21

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**User Contributed Comments**
3

User |
Comment |
---|---|

nedved19 |
Is Expected alpha = ex ante alpha and Realized alpha = ex post alpha? |

soorajiyer |
@nedved ex ante alpha = expected return - required return ex post alpha = historical HPR for the security - historical HPR for similar security. Hope this helps! |

bablig |
Ex post alpha is the difference between historical realized return and required return. The diff between Ex Ante and Ex Post is that for the former we take expected return and for the latter we take realized return. But the comparison is with Expected return for both. |

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