The CAPM

The CAPM

The Capital Asset Pricing Model Ming Liu Industrial Engineering and Management Sciences, Northwestern University Winter 2009 Returns to financial securities P0: security price at time 0 P1: security price at time 1 DIV1: dividend at time 1 r = total return = dividend yield + capital gain

rate r = DIV1/P0+(P1-P0)/P0 (random variable) ri : the return on security i, Decompose this return ri into that part correlated with the market and that part uncorrelated with the market rm = the return on the market portfolio i = the specific return of firm i Systemic and Idiosyncratic Risk

ri=i+ i rm + i systemic risk undiversifiable risk beta risk market risk idiosyncratic risk diversifiable risk non-systematic risk "Beta" ) an asset market risk parameter, represents straight-line inclination degree. E is average "residual" yield, describing an average asset yield deviation from "fair" yield as

shown by the central line. ri=i+i rm +i The larger is i , the more subject to market risk is this firm. The larger is [i] the more important is firmspecific risk. 2 i 2 [ri ] [rm ] ( [ i ])

2 Example Decomposing the Total Risk of a Stock Considering two stocks: 2 [ ] .10

A: An automobile stock with A=1.5, A 2 [ ] .18 B B: An oil exploration company with B=0.5, 2

[ r ] .04 m The variance of the market return is What is the total risk of each stock? [rA ]2 1.52 0.04 0.10 0.19 [rB ]2 0.52 0.04 0.18 0.19 Which has a higher expected rate of

return? Portfolio risk 1. Decompose each security return into systematic and idiosyncratic risk: ri=i+irm+i 2. Form a portfolio of these securities, with portfolio weights w1, w2, , wn . (sum to one) 3. The portfolio rate of return is a weighted average of the individual returns rp = w1r1+w2r2++wnrn

rp = w1[1+1rm+1] + w2[2+2rm+2] + + wn[n+nrm+n] Rearrange to get zero rp = *+*rm+*, where *:= w11+w2 2++wn n *:= w1 1+w2 2++wn n

*:= w1 1+w2 2++wn n Conclusions of portfolio is weighted-average Well diversified -> risk only from rm term The standard deviation of a well diversified portfolio: [rp ] * [ rm ] Construct the market portfolio The market portfolio includes every security in the market

The weight of each security in the portfolio is proportional to its relative size in the economy A common proxy measure for the market portfolio is the S&P 500 index. http://www.indexarb.com/indexComponentWtsSP 500.html The Capital Asset Pricing Model Market model ri=i+irm+i with i=(1-i) rf

ri=(1-i) rf+irm+i ri=(1-i) rf+irm+i Does this restricted case make sense? What does it imply for the return on a risk-free asset (i=0)? What does it imply about the return on an asset that has the same market risk as the market portfolio (i=1)? The CAPM equation can be rewritten as ri-rf=i (rm rf )+i

The CAPM can also be written as a linear relationship between the of a security and its expected rate of return, E(ri )-rf=i (E (rm )rf ) E(ri ) : expected rate of return on the security E (rm): expected rate of return on the market portfolio rf : the risk free rate i : the securitys beta The Security Market Line

E(ri ) E(ri )=rf+i (E (rm )rf ) E(ri )=(1- i)rf+i E (rm ) E(rA ) E(rB ) rf B=0.5 A=1.5

i Example Using the Security Market Line (SML) The of Cisco Systems is about 1.37. The risk free rate rf=0.07 Expected risk premium on market E (rm )rf =0.06 The expected rate of return on CSCO: E (ri ) 0.07 1.37 0.06 0.1522 How to get ?

If we know [ri] ----- standard deviation of ri [rm] ----- standard deviation of rm im----- correlation between ri and rm cov(ri , rm ) im [ri ] [rm ] im [ri ] i 2 2 [rm ]

[rm ] [rm ] How to get ? im [ri ] Estimate beta: i [rm ]

ri=i+ i rm + i http://finance.yahoo.com/ CAPM serves as a benchmark Against which actual returns are compared Against which other asset pricing models are compared Advantages: Simplicity Works well on average

Disadvantages: What is the true market portfolio and risk free rate? How do you estimate beta? Standard deviation not a good measure of risk.

Recently Viewed Presentations

  • Filozofijas Pamati

    Filozofijas Pamati

    Kāds ir Jūsu viedoklis? Otrs problēmu loks ir agresivitāte: cilvēks zaudē kontroli pār savu kustību spēju, kā arī parādās parunāt nespējas problēma, vienkārši vairs-saprasties-nespēja. Cilvēki savstarpēji nevar īsti ieklausīties, runā viens otram garām - ja vispār vēl atrod vārdus tam,...
  • 2015 IASA CAROLINAS CHAPTER MEETING WAKE FOREST UNIVERSITY

    2015 IASA CAROLINAS CHAPTER MEETING WAKE FOREST UNIVERSITY

    Evidence that card holder data only resides in the card holder data environment. Proof via Data flow documentation. Interviews with business process owners. Automated scans at perimeter points. Proof of data containment. Image courtesy of PCI SSC. Requirements that organizations...
  • Microwave Engineering

    Microwave Engineering

    It seem the impedance characteristic is maintain. Attenuator (transmission mode) Attenuator (Reflection mode) Diode ON-attenuated Diode OFF- transmitted * V-I characteristic Equivalent circuit where a= q /nkT , q =charge, k=Boltzmann's constant, T = temperature, n = ideality factor and...
  • Accessible Design is Sustainable Design

    Accessible Design is Sustainable Design

    The Egan Wheel. Governance. Transport & Connectivity. Services. Environmental. Equity. Economy. Housing & Built Environment. Social & Cultural
  • Flag Burning and the First Amendment

    Flag Burning and the First Amendment

    The Flag Protection Act of 1969 Whoever knowingly casts contempt upon any flag of the United States by publicly mutilating, defacing, defiling, burning, or trampling upon it shall be fined not more than $1,000 or imprisoned for not more than...
  • Statistique 51-601-96 COURS # 4

    Statistique 51-601-96 COURS # 4

    The squared correlation coefficient is called the coefficient of determination and the percentage of the variability of Y explained by X: R2 = 1 - (n-2)/(n-1){Se /Sy}2, where Se is the standard deviation of the errors and Sy is the...
  • Frank Luntz is the premier language consultant to

    Frank Luntz is the premier language consultant to

    * * * * Frank Luntz is the premier language consultant to conservative Republicans. Luntz Research, Inc. offers Focus Groups, Surveys, Instant Response, and Strategic Consulting.
  • 슬라이드 1 - Snu

    슬라이드 1 - Snu

    SOC Design Conference SoC Verification Strategies for Embedded Systems Design November 5-6, 2003/ Seoul Chong-Min Kyung, KAIST