Risk & Return Three hypothetical stocks Javier Go Estrada - - PDF document

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Risk & Return Three hypothetical stocks Javier Go Estrada - - PDF document

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Corporate Finance Risk, Return, Diversification, and the CAPM Javier Estrada Spring, 2014 1. Risk & Return Return, mean return, and volatility 2. Diversification Four viewpoints on diversification Essential variables in portfolio

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  • 1. Risk & Return
  • Return, mean return, and volatility
  • 2. Diversification
  • Four viewpoints on diversification
  • Essential variables in portfolio construction
  • The critical role of correlation
  • 3. Risk Revisited
  • Nonsystematic risk, systematic risk, and beta
  • 4. The CAPM
  • Notation and overview

Corporate Finance

Risk, Return, Diversification, and the CAPM

Javier Estrada Spring, 2014

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Risk & Return

  • Three hypothetical stocks

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  • Returns

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  • Summarizing performance
  • Arithmetic mean return

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 Interpretation (Backward / Forward)  Evidence (Workout)

  • Standard deviation (Volatility)

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 Interpretation (Uncertainty)  Evidence (Workout)

  • Risk aversion

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

  • Why do investors combine assets?
  • Viewpoint 1
  • To avoid ‘losing everything’

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  • Viewpoint 2
  • To reduce volatility

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 More formally, to minimize the portfolio’s risk for a target level of return  Technically, this yields the minimum variance set

  • Correlation
  • Formal/theoretical aspects
  • Evidence (Workout)
  • Practical relevance
  • Very far from a ‘statistical thing’

Go Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Portfolio Construction

  • Relevant variables
  • Portfolio return v. Weighted average of returns
  • Portfolio risk v. Weighted average of risks

GoXls

  • In general (unless assets have ρ=1)

 Portfolio risk < Weighted average of risks  Therefore, when combining assets, we average returns but less than average risks

  • Spain v. China
  • Feasible set, minimum variance set, minimum

variance portfolio (MVP), and efficient set

  • Gains from diversification

Go

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification Again

  • One more viewpoint
  • Viewpoint 3
  • To maximize the portfolio’s expected return for a

target level of risk

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 Technically, this yields the efficient set

  • Important question
  • Why would a Chinese investor want to diversify?
  • What is his ultimate benefit?

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  • One final viewpoint
  • Viewpoint 4
  • To maximize the portfolio’s risk‐adjusted return

 This is optimal for both (Spanish/Chinese) investors

Go Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Risk

  • So far, risk is measured by volatility (SD)
  • This is the total risk of an asset
  • What factors determine this total risk?
  • Nonsystematic factors
  • Diversification reduces nonsystematic risk
  • Systematic factors
  • Diversification does not reduce systematic risk

 Then, the benefits from diversification are limited

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  • Four complementary comments
  • n* changes over time and across markets

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  • International diversification

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  • Asset‐class diversification

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  • Keep in mind the ultimate goal

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Risk Redefined

  • Risk depends on the context in which the asset is

evaluated

  • Asset in isolation
  • Risk = σi (Volatility)

 A measure of total risk

  • Asset within a diversified portfolio
  • Risk = βi (Beta)

 A measure of systematic risk  A measure of relative volatility  Widely and publicly available

Go Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

The CAPM

  • The Capital Asset Pricing Model is given by …
  • Ri = Rf + MRP·βi
  • This expression is called the securities market line

(SML) and is plotted on the R‐β space

  • Comments
  • Ri is the required or expected return of asset i
  • Rf is the risk‐free rate
  • Compensation for the expected loss of purchasing

power

  • MRP·βi = RP is the risk premium
  • Compensation for bearing risk

 MRP is the market risk premium (Compensation for investing in risky equity rather than in risk‐free debt)  βi is the asset’s beta (A measure of systematic risk)

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

The CAPM

  • Empirically
  • Rf = 3.0% (Jan/1/2014)
  • MRP = 5.5% (Historical / USA)
  • Therefore, …
  • Ri = 3.0% + (5.5%)·βi
  • Two important properties of the CAPM
  • The beta of a portfolio is equal to the weighted

average of the betas of the assets in the portfolio

  • βp = x1·β1 + x2·β2 + … + xn·βn
  • In equilibrium, all assets should be priced in such a

way so that their risk and return fall along the SML

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Appendix

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Prices & Dividends

Back Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Returns, Mean Return, & Volatility

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Volatility

Back

SD1: 10% SD2: 1.5% SD3: 5%

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Risk Aversion

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back

Risk Aversion

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

  • Consider the following portfolio
  • 13% in stock 1 and 87% in stock 2

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

  • Consider now the following portfolio
  • 50% in stock 1 and 50% in stock 3

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Diversification

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Correlation

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Correlation

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Correlation

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Correlation

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

CHN SPA

39.0% 11.9% 28.1% 19.6%

Correlation = 0.60

(27.8% , 12.9%) (28.1% , 13.9%)

Annual Diversification Gain = 2.0%

Back Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

Back Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

CHN SPA

39.0% 11.9% 28.1% 19.6%

Correlation = 0.60

(27.8% , 12.9%) (28.1% , 13.9%)

Annual Diversification Gain = 2.0%

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Gains from Diversification

Back

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Limits to Diversification

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How Many Stocks?

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How Many Stocks?

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International Diversification

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International Diversification

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Asset‐Class Diversification

DMs – 2008 EMs – 2008

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Asset‐Class Diversification

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Asset‐Class Diversification

Back

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Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Remember!

Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014

Remember!

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