Question

Outline the general regression equation for a single index model and, from this,
outline the expected return-beta relationship. Explain what is meant by the Security
Characteristic Line, making reference to the alpha and beta estimates.

Answer 1

The answer is as follows:

Assumption of Single Indone Model There is only one mocioeconomic factor that causes the systematic risk affecting all stock returns and this factor can be represented by the rate of return on a market index. Application of Single Inder Model: According to this model, the return of any stock can be decomposed into three factors! A. Expected return of the individual stock due to firm-specific factors, B. Expected return of the individual stock due to market factors and C. Return of individual stock due to unexpected microeconomic events that affect only the firm. Expression of Single Inder Model for o Stock: Es = 2; + B: *{Erm) tei

Construction of Single Index Model for a stock. • In order to create the single indos modelo historic returns on a broad index and the Stock for corresponding beriods are considered. • Subsequently, the returns from the stock (dependent variable) wee regressed on the returns from the inder (independent variable). Classification of Risk under Single Inder Model: Systematic Rick I t » Total Risk. Unsystematic Risk Calculation of Risk of a stock : • Systemati Lick : (B: 46m)? • Total Risk : 62 • Hence, Unsystematic Risk: 8² - ( b *6m) 2 which is also referred to as (bei) ? Concept of Beta : • Beto is a quantitative measure of volatility,

for systematic risk of a given stock, mutual fund. or portfolio in comparison to the market. as a whole. One can think of beta as the tendency of a security's returns to respond to swings in the market. Calculation of Bela : • B; -(676m) * (im) L. B; = ( Er; - RF)/(Erm-RE) B; = (Enje - Erja) / (Erre- Erma) Ealooession of Single Index Model for o Portfolio : • Exp = dp + B * (Erm) + epo Construction of single Indera Model: + Alpha of a Pootfólios E (Nit Xi) → Bela of a Portfolio = {(Witt fi) Calulation of Risk of Portfolio : · Systematic Risk : (Bp+ m)2 • Unlystematic Risk : ( 6ep)?- <[CW1:72 *(Q;)2] = [(Wi)? * USYSRSK STK 7

• Total Riskirp = (Systematic Risk + Unsystematic Risk The Securities Characteristics Line : The goophical representation of the returns of the stock corresponding to different retwers of the inden is known as the Securities Characteristics Line. - This is always represented by a straight line. Goophical Representation of Single Indes Model: ER * Beta (B) Alpha (a) 2 ERM