We know that exchange rate volatility affects the volatility of the dollar return on a foreign stock. This is because it is not the Sharpe ratio of the foreign asset that the U.S.
How to Diversify at Home
O PTIMAL P ORTFOLIO A LLOCATION
The correlation figure is taken from Appendix 13.6; the volatility figures (in dollars) are taken from Appendix 13.1 (both for the US and the foreign country); rf is set to 5%; and E[r] is the United States. We can represent the investor's feasible portfolios by a number of wealth fractions – proportions of wealth allocated to each asset – and these proportions must be added to 1.
Preferences
Once we expand the components to multiple risky assets, we can solve the portfolio problem. For example, we will find that no smart investor should ever choose the 50–50 portfolio we proposed.
The Case of One Risky Asset
If the proportion w of the portfolio is invested in the risky asset, then 1 - w is invested in the risk-free asset. As risk aversion increases, the weight on the risky asset decreases, lowering the expected return and the standard deviation.
The Mean–Standard Deviation Frontier
Assumptions and Origins
A Derivation of the CAPM (Advanced)
The correlation of the new asset's return with rp, which now contains some new asset, increases as more new asset is added, making the condition more difficult to meet. At this point, further additions no longer increase the Sharpe ratio; that is, we have reached the portfolio that maximizes the Sharpe ratio, which means that we have found the MVE portfolio. If we rewrite equation (13.4) using the definition of the Sharpe ratio and bring r to the other side, we get.
3E1rp2 - rf4 (13.6) Equation (13.6) establishes a relationship between the expected excess return on an individual asset and the expected return on the MVE portfolio. If a risk-free asset exists, a portfolio of risky securities offers the best risk-return trade-off: the MVE portfolio. Now, if everyone is a mean-variance investor facing the same limit, what should the MVE portfolio be so that there is no excess demand or supply for any security.
The relationship between the expected return on an individual security and the expected return on the market portfolio depends on the statistical construct Cov1ri, rm2.
Interpreting the CAPM
The risk premium on the market portfolio is the amount by which the expected return on the market exceeds the risk-free interest rate. The CAPM actually predicts that this risk premium will depend on the average risk aversion of investors and the variance of the market portfolio return. Therefore, the market risk premium balances the variance of the market portfolio to reflect the average risk aversion of the investors in the market.
Equity returns that vary positively with the return on the market portfolio contribute to the variance of the return on the market portfolio. On the other hand, an asset with a negative beta whose return varies negatively with the market return. Note that an asset's beta measures its relative risk because beta is the covariance of the asset's return with the return on the market portfolio divided by the variance of the return on the market portfolio.
For example, if the beta is 1, the covariance of the asset's return with the market portfolio return is equal to the variance of the market's return, and the expected return of the asset is the same as the expected return of the market.
Domestic Versus World CAPMs
As discussed in detail in Chapter 15, firms need expected returns on equity to obtain appropriate discount rates in capital planning. These expected returns represent what investors demand in return for providing capital to the company.
A Recipe for the Cost of Equity Capital
Get data on the market portfolio's return, the share return on security j , and the treasury rate, rf.
The Benchmark Problem The Market Portfolio
To calculate the error when using equation (13.13) instead of equation (13.12), we first calculate the correct expected return on the home market portfolio. Stulz estimates that the beta of the Swiss franc return on Nestlé relative to the Swiss franc return on the Swiss market portfolio 1bjh2 is 0.885. The beta of the Swiss franc return on Nestlé relative to the Swiss franc return on the 1bjm2 World Market Portfolio using the FTA World Market Index is 0.585.
The beta of the Swiss franc return on the Swiss market portfolio relative to the Swiss franc return on the world market portfolio 1bhm2 is 0.737. If Nestlé is priced in the world market and not the local market, its expected return should be the risk-free return on Swiss franc bonds plus a risk premium equal to the beta of the world market portfolio multiplied by the excess return per share. the world market portfolio. If Nestlé is priced in the local market, its expected return will be the risk-free return on Swiss franc bonds plus a risk premium equivalent.
Estimation errors in the betas and average global market portfolio returns can easily lead to discount rates within this range being considered when conducting sensitivity analyses.
Beta Estimation
The Risk Premium on the Market Historical Estimates
I NTEGRATED V ERSUS S EGMENTED M ARKETS
Investing in Emerging Markets
In this section, we first discuss investing in emerging markets and the critical role of investment barriers. Correlations vary between 0.08 for Argentina and Japan and 0.61 for Hungary with Great Britain and Germany. The lowest correlations are typically observed with Japan, with the exception of Korea, which is more correlated with its close neighbor than with the other developed markets.
Not surprisingly, early studies found significant diversification benefits for investing in emerging markets. More generally, older data may no longer be relevant as many emerging markets imposed strict investment restrictions on foreign investors in the early 1990s. These results suggest that investment barriers may prevent the diversification benefits of emerging markets from being fully realized.
Emerging markets in particular may not be fully integrated with world capital markets, making the world CAPM the wrong model to use.
The Cost of Capital in Integrated and Segmented Markets
We know that bj is the covariance of security j with the market portfolio; thus, we can rewrite equation (13.15) as. Therefore, in segmented markets, expected and hence mean returns should be related to the variance of returns rather than covariance with the world market return. If liberalization leads to integration with the global capital market, and if the world CAPM holds, what do we expect to happen?
Also, the risk premiums associated with the shares in that country will be determined by the variance of the return on the market portfolio of that country. 8 Second, the country's stocks will now be priced based on their covariances with global market portfolio returns, which are likely to be much smaller than the local market variance. Even with this effect, it is likely that these covariances will remain much smaller than the local market variance.
Second, the correlation of the return and its beta with the world market increases after the liberalization of the stock market, and for some countries the increase is dramatic.
Segmentation and Integration over Time
In evaluating PT Semen Gresik in 1998, you need to determine an appropriate discount rate. The historical average rate of return will reflect both the high risk premium, typical of securities in segmented countries, and the one-time capital gain that occurred when Indonesia opened its international capital market. Therefore, the beta of PT Semen Gresik's returns relative to the world market, calculated with post-1990 data, is likely to enter the calculation as well.
Because no data is available, the amount of risk premium to add to the risk-free rate becomes a business judgment. The equity risk premium should be based on the type of company the project represents. If the business is highly cyclical and profits are likely to vary with the return on a global market portfolio, you are adding more than the average risk premium.
In this case, it is likely that China's power plant cash flows show little correlation with the world market and that a low risk premium is required.
Home Bias and Its Implications
The normalized measure of house bias divides the raw measure by 1 - the weight of the world market benchmark, which is nothing more than the maximum bias that can occur. A fully home biased country has a normalized measure of 1, while a country that invests in its own market in line with its world market share has a home bias measure of zero. First, around the world, people hold far fewer foreign securities than the CAPM world would dictate.
Investors do not appear to be taking full advantage of the significant benefits of international diversification. Finally, it is common knowledge that the degree of domestic bias has decreased significantly over time. Cai and Warnock (2006) argue that the degree of home bias is overestimated because institutional investors tend to overweight their domestic investments in multinationals that have international exposure through their foreign operations and cash flows.
Even if we adjust the numbers for this additional foreign exposure, domestic bias remains significant for most countries in the world and is something that is not well understood by financial economists.
What Breeds Foreign Investment?
A LTERNATIVE C OST - OF -C APITAL M ODELS
The Usefulness of the CAPM
Given that the CAPM can be wrong and that recent empirical tests have not been good against the CAPM, there is an alternative model for calculating the cost of capital.
Factor Models and the Fama-French Model
S UMMARY This chapter develops the theories and background nec-
Ang, Andrew, Robert Hodrick, Yuhang Xing en Xiaoyan Zhang, 2006, "The Cross-Section of Volatility and Expected Returns," Journal of Finance 61, pp. Brooks, Robin en Marco Del Negro, 2004, "The Rise in Mede-beweging oor nasionale aandelemarkte: markintegrasie of IT-borrel?” Journal of Empirical Finance 11, pp. Dimson, Elroy, Paul Marsh en Mike Staunton, 2007, "The Worldwide Equity Premium: A Smaller Puzzle," in Rajnish Mehra, ed., Handbook of the Equity Risk Premium, Amsterdam: Elsevier Science, pp.
Dumas, Bernard and Bruno Solnik, 1995, "The World Price of Foreign-Exchange Risk," Journal of Finance 50, pp. Lettau, Martin, Sydney Ludvigson, and Jessica Wachter, 2008, "The Declining Equity Premium: What Role Does Macroeconomic Risk Play?" Review of Financial Studies 21, pp. Lintner, John, 1965, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgeting," Review of Economics and Statistics 47, pp.
Stulz, René M, 1995, "The Cost of Capital in Internationally Integrated Markets: The Case of Nestlé," European Financial Management 1, pp.
