2015, Study Session # 12, Reading # 43

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“PORTFOLIO RISK AND RETURN: PART II”

43.a

� In reading 44 we determined E (RP) & σP of combined assets (risky & RF).

� Risk return tradeoff can be plotted through a line started with RF return &

extend through the risky portfolio.

SML = Securities Market Line

FR = Forecasted Return

RR = Required Return

MPT = Market Portfolio Theory

BV = Book Value

MV = Market Value

RF = Risk Free

CML = Capital Market Line

SR = Systematic Risk

NSR = Non systematic

CAL = Capital Allocation Line

EF = Efficient Frontier

43.b

��� = ����� = �� + �����− ��� ��

� For an individual investor best CAL should represent best risk / return combination

(greatest utility).

� MPT assume homogenous expectations (same EF, risky portfolio (market portfolio) &

CAL).

� Optimal CAL (CML) ⇒ tangent to EF.

where

intercept is Rf & slope is ��������

��

� Diff. b/w E (RM) & Rf is market risk premium.

� If investors can borrow at RF, they can invest to the right of the market portfolio.

Investment Strategies

Passive Active

� When investor believes markets

are efficient.

� Index investment.

� Markets are not informationally

efficient.

� Overweight the undervalued &

underweight the overvalued

securities to generate active

return.

43.c � Not perfectly correlated assets ⇒ portfolio risk <

weighted avg. risk of portfolio’s securities.

� Total risk = systematic risk + nonsystematic risk.

Types of Risk

Nonsystematic Risk Systematic Risk

� Also known as idiosyncratic,

diversifiable or firm specific risk.

� Eliminated through diversification.

� No need to buy all market securities

to eliminate N.S.R.

� N.S.R. is not compensated in

equilibrium (can be eliminated for

free through diversification).

� Also known as non diversifiable or

market risk.

� Can’t be eliminated through

diversification.

� Concept applies to individual

securities as well as portfolios.

� Firms highly correlated with market

� S.R.

� High total risk does not necessarily

mean � expected return.

2015, Study Session # 12, Reading # 43

Copyright © FinQuiz.com. All rights reserved.

43.d

�����− �� = �� × ��������1� + ��� × ��������2� + … + ��� × ����������

����� − �� = �������� − ���

� Return generating models ⇒ to estimate E(R) on risky securities based on specific

factors (macroeconomic, fundamental & statistical).

� Multifactor models ⇒ use macroeconomic statistical & fundamental factors.

� Statistical factors represent relations for specific time period.

� Fama & French model consider three factors; firm size, BV/MV ratio & beta, Carhart

include 4th

factor as momentum.

� Market model is a single factor model

where β represent sensitivity of return of ������ to return on market portfolio.

43.e

����������������� ������!����������������� ��"��ℎ���#����� ��$

�� = %��

��

� �� = ��������

Using correlation

� Slope of least squares regression line (best fit) is the estimate of β.

43.f

����� = �� + ��������− ��� � SML ⇒ line that represent relationship b/w S.R (β) & return.

� SML equation (CAPM)

Comparison b/w CML & SML

CML SML

� Use total risk (only efficient

portfolios at CML).

� Use β (all properly priced

securities & portfolios plot on

SML).

Low β stock is not necessarily low risk stock (when total risk is a consideration).

2015, Study Session # 12, Reading # 43

Copyright © FinQuiz.com. All rights reserved.

43.g

CAPM = equilibrium model that predicts E(R) on a stock given E (Rm), β & RF.

43.h

� In equilibrium, security’s E(R) is equal to its required return.

� Analyst can compare forecasted return with required return if;

FR > RR ⇒ security is undervalued (plot above the SML).

FR < RR ⇒ security is overvalued (plot below the SML).

FR = RR ⇒ security is fairly valued (plot on SML).

Risk-adjusted return measures (β)

Treynor measure Jensen’s Alpha

� ��&� &������ ����

��

Excess return per unit of systematic risk.

� Does not work for –ve β assets.

� % return in excess of those from a

portfolio with same β but lies on SML.

� α� = �� − ��� + ��'�� − ��(�

� If portfolio is not fully diversified, total risk is more relevant and, Sharpe ratio or M2 is

appropriate measure.

� If portfolio is well-diversified and diversifiable risk is negligible Treynor & Jensen’s alpha

are appropriate.

� These measures are used to compare actively managed fund’s performance with passively

managed funds.

Total Risk Adjusted Return Measure

Sharpe Ratio M-Squared

�ℎ��)������ = *�� − ��� + ��,������� ��)�� ���������&)�����&�����#. � sharpe ratio is a relative measure & slope of CML & CAL.

�����)�����&����#��-���ℎ��)�������. � � − ./ �������� = '�� − ��( ��

��− '�� − ��(