Question

a. Fama’s return decomposition has two main components –i)Risk and ii) Selectivity. Risk is further sub-divided into Investor’s Risk and Manager’s Risk. Selectivity is also sub-divided into Diversification and Net Selectivity. Explain in detail each element and what role do they play in decomposing portfolio performance.

b. The following market and portfolio performance and risk characteristics are given below. Based on the information provided, calculate all four components of portfolio performance.

Risk-free rate =2.5%

Market return= 12%

Market standard deviation = 0.14

Portfolio return = 14%

Portfolio target beta = 1.1

Portfolio actual beta = 1.2

Portfolio standard deviation = 0.18

Answer 1

Answer to (a)
Explanations
Risk
This is the portion of the excess return that is explained by the portfolio beta and the market risk premium:	RP(Risk)	=	Beta of portfolio (return of Market - Risk Free Rate)
Investor’sRisk
If an investor specifies a particular target level of risk (i.e., beta) then we can further decompose the risk premium due to risk into investor’s risk and manager’s risk.n Investors risk is the risk premium that would have been earned if the portfolio beta was exactly equal to the target beta:	RP(Investor Risk	=	Target Beta (Return of market - Risk Free Rate)
Manager’sRisk
If the manager actually takes a different level of risk than the target level (i.e., the actual beta was different than the target beta) then part of the risk premium was due to the extra risk that the manager’s took	RP(Manager Risk)	=	(Actual Beta - target Beta)(Return of market - Risk Free Rate)
Selectivity
This is the portion of the excess return that is not explained by the portfolio beta and the market risk premium:n Since it cannot be explained by risk, it must be due to superior security selection.	RP(Selectivity)	=	RP (Total)- RP(Risk)	=	RP (Total)- Beta of portfolio(Return of Market - Risk free Rate)
Diversification
This is the difference between the return that should have been earned according to the CML and the return that should have been earned according to the SMLn If the portfolio is perfectly diversified, this will be equal to 0	RP(Diversification)	=	{Return of Market - risk Free Rate}(S.D of Portfolio/ S.D. of Market - Actual Beta)
Net Selectivity
Selectivity is made up of two components: ¡ Net Selectivity ¡ Diversificationn Diversification is included because part of the manager’s skill involves knowing how much to diversifyn We can determine how much of the risk premium comes from ability to select stocks (net selectivity) by subtracting diversification from selectivity.
Answer to (b)
RP(Risk)	=		Beta of portfolio (return of Market - Risk Free Rate)
	=		1.2 (12.5%-2.5%)
	=		12
RP(Investor Risk	=		Target Beta (Return of market - Risk Free Rate)
	=		1.1 (12.5%-2.5%)
	=		11
RP(Manager Risk)	=		(Actual Beta - target Beta)(Return of market - Risk Free Rate)
	=		(1.2-1.1)(12.5%-2.5%)
	=		1
RP(Selectivity)	=		RP (Total)- RP(Risk)	=	RP (Total)- Beta of portfolio(Return of Market - Risk free Rate)
				=	12- 1.2 (12.5%-2.5%)
				=	0
RP(Diversification)	=		{Return of Market - risk Free Rate}(S.D of Portfolio/ S.D. of Market - Actual Beta)
	=		{12.5%-2.5%}(0.18/0.14-1.2)
	=		0.85