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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

  1. 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 construction • The critical role of correlation 3. Risk Revisited • Nonsystematic risk, systematic risk, and beta 4. The CAPM • Notation and overview Risk & Return  Three hypothetical stocks Javier Go Estrada  Returns IESE Go Business  Summarizing performance School Barcelona • Arithmetic mean return Go Spain  Interpretation (Backward / Forward)  Evidence (Workout) • Standard deviation (Volatility) Go  Interpretation (Uncertainty)  Evidence (Workout)  Risk aversion Go MBA CorpFin Spring, 2014 1

  2. Diversification  Why do investors combine assets? Javier Estrada  Viewpoint 1 IESE Business • To avoid ‘losing everything’ School Go  Viewpoint 2 Barcelona Spain • To reduce volatility Go  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’ MBA Go CorpFin Spring, 2014 Portfolio Construction  Relevant variables Javier Estrada  Portfolio return v . Weighted average of returns IESE Business  Portfolio risk v . Weighted average of risks School GoXls Barcelona • In general (unless assets have ρ=1) Spain  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 MBA CorpFin Spring, 2014 2

  3. Diversification Again  One more viewpoint Javier Estrada  Viewpoint 3 IESE Business • To maximize the portfolio’s expected return for a School target level of risk Barcelona Go Spain  Technically, this yields the efficient set  Important question  Why would a Chinese investor want to diversify? • What is his ultimate benefit? Go  One final viewpoint  Viewpoint 4 • To maximize the portfolio’s risk ‐ adjusted return  This is optimal for both (Spanish/Chinese) investors Go MBA CorpFin Spring, 2014 Risk  So far, risk is measured by volatility (SD) Javier Estrada  This is the total risk of an asset IESE Business  What factors determine this total risk? School Barcelona  Nonsystematic factors Spain • Diversification reduces nonsystematic risk  Systematic factors • Diversification does not reduce systematic risk  Then, the benefits from diversification are limited Go  Four complementary comments  n * changes over time and across markets Go  International diversification Go  Asset‐class diversification Go MBA  Keep in mind the ultimate goal CorpFin Go Spring, 2014 3

  4. Risk Redefined  Risk depends on the context in which the asset is Javier Estrada evaluated IESE Business  Asset in isolation School Barcelona • Risk = σ i (Volatility) Spain  A measure of total risk  Asset within a diversified portfolio • Risk = β i (Beta)  A measure of systematic risk  A measure of relative volatility  Widely and publicly available Go MBA CorpFin Spring, 2014 The CAPM  The Capital Asset Pricing Model is given by … Javier Estrada  R i = R f + MRP· β i IESE Business • This expression is called the securities market line School (SML) and is plotted on the R ‐ β space Barcelona Spain  Comments  R i is the required or expected return of asset i  R f is the risk‐free rate • Compensation for the expected loss of purchasing power  MRP· β i = 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) MBA  β i is the asset’s beta (A measure of systematic risk) CorpFin Spring, 2014 4

  5. The CAPM  Empirically Javier Estrada  R f = 3.0% (Jan/1/2014) IESE Business  MRP = 5.5% (Historical / USA) School  Therefore, … Barcelona Spain • R i = 3.0% + (5.5%)· β i  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 • β p = x 1 · β 1 + x 2 · β 2 + … + x n · β n  In equilibrium, all assets should be priced in such a way so that their risk and return fall along the SML MBA CorpFin Spring, 2014 Appendix Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 5

  6. Prices & Dividends Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back Returns, Mean Return, & Volatility Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back 6

  7. Volatility Javier Estrada SD1: 10% IESE Business School Barcelona Spain SD2: 1.5% MBA SD3: 5% CorpFin Spring, 2014 Back Risk Aversion Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 7

  8. Risk Aversion Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back 8

  9. Diversification  Consider the following portfolio Javier Estrada  13% in stock 1 and 87% in stock 2 IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 9

  10. Diversification  Consider now the following portfolio Javier Estrada  50% in stock 1 and 50% in stock 3 IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back 10

  11. Correlation Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Correlation Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 11

  12. Correlation Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Correlation Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back 12

  13. Gains from Diversification Javier Estrada IESE Annual Diversification Gain = 2.0% CHN Business School 19.6% Barcelona Spain (28.1% , 13.9%) (27.8% , 12.9%) SPA Correlation = 0.60 11.9% 28.1% 39.0% MBA CorpFin Spring, 2014 Back Gains from Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 13

  14. Gains from Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back Gains from Diversification Javier Estrada IESE Annual Diversification Gain = 2.0% CHN Business School 19.6% Barcelona Spain (28.1% , 13.9%) (27.8% , 12.9%) SPA Correlation = 0.60 11.9% 28.1% 39.0% MBA CorpFin Spring, 2014 Back 14

  15. Gains from Diversification 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 Back 15

  16. Limits to Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back How Many Stocks? Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 16

  17. How Many Stocks? Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back International Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 17

  18. International Diversification Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back Asset ‐ Class Diversification Javier Estrada IESE Business School Barcelona Spain DMs – 2008 EMs – 2008 MBA CorpFin Spring, 2014 18

  19. Asset ‐ Class Diversification 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 Back 19

  20. Remember! Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Remember! Javier Estrada IESE Business School Barcelona Spain MBA CorpFin Spring, 2014 Back 20

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