【導讀】ChapterOpener. PART  II. p.196. p.197

　　

【正文】 securities might best be constructed.The Optimal Risky Portfolio with Two Risky Assets and a RiskFree AssetWhat if our risky assets are still confined to the bond and stock funds, but now we can also invest in riskfree Tbills yielding 5%? We start with a graphical solution.Figure shows the opportunity set based on the properties of the bond and stock funds, using the data fromTable .Figure The opportunity set of the debt and equity funds and two feasible CALsTwo possible capital allocation lines (CALs) are drawn from the riskfree rate (rf= 5%) to two feasible portfolios. The first possible CAL is drawn through the minimumvariance portfolioA,which is invested 82% in bonds and 18% in stocks (Table , bottom panel, last column). PortfolioA39。s expected return is %, and its standard deviation is %. With a Tbill rate of 5%, therewardtovolatility (Sharpe) ratioRatio of excess return to portfolio standard deviation.,which is the slope of the CAL bining Tbills and the minimumvariance portfolio, isNow consider the CAL that uses portfolioBinstead ofA.PortfolioBinvests 70% in bonds and 30% in stocks. Its expected return is % (a risk premium of %), and its standard deviation is %. Thus the rewardtovolatility ratio on the CAL that is supported by portfolioBiswhich is higher than the rewardtovolatility ratio of the CAL that we obtained using the minimumvariance portfolio and Tbills. Hence, portfolioBdominatesA.p. 207WORDS FROM THE STREETRecipe for Successful Investing: First, Mix Assets WellFirst things first.If you want dazzling investment results, don39。t start your day foraging for hot stocks and stellar mutual funds. Instead, say investment advisers, the really critical decision is how to divvy up your money among stocks, bonds, and supersafe investments such as Treasury bills.In Wall Street lingo, this mix of investments is called your asset allocation. “The assetallocation choice is the first and most important decision,” says William Droms, a finance professor at Georgetown University. “How much you have in [the stock market] really drives your results.”“You cannot get [stock market] returns from a bond portfolio, no matter how good your security selection is or how good the bond managers you use,” says William John Mikus, a managing director of Financial Design, a Los Angeles investment adviser.For proof, Mr. Mikus cites studies such as the 1991 analysis done by Gary Brinson, Brian Singer and Gilbert Beebower. That study, which looked at the 10year results for 82 large pension plans, found that a plan39。s assetallocation policy explained % of the return earned.DESIGNING A PORTFOLIOBecause your asset mix is so important, some mutual fund panies now offer free services to help investors design their portfolios.Gerald Perritt, editor of theMutual Fund Letter,a Chicago newsletter, says you should vary your mix of assets depending on how long you plan to invest. The further away your investment horizon, the more you should have in stocks. The closer you get, the more you should lean toward bonds and moneymarket instruments, such as Treasury bills. Bonds and moneymarket instruments may generate lower returns than stocks. But for those who need money in the near future, conservative investments make more sense, because there39。s less chance of suffering a devastating shortterm loss.SUMMARIZING YOUR ASSETS“One of the most important things people can do is summarize all their assets on one piece of paper and figure out their asset allocation,” says Mr. Pond.Once you39。ve settled on a mix of stocks and bonds, you should seek to maintain the target percentages, says Mr. Pond. To do that, he advises figuring out your asset allocation once every six months. Because of a stockmarket plunge, you could find that stocks are now a far smaller part of your portfolio than you envisaged. At such a time, you should put more into stocks and lighten up on bonds.When devising portfolios, some investment advisers consider gold and real estate in addition to the usual trio of stocks, bonds and moneymarket instruments. Gold and real estate give “you a hedge against hyperinflation,” says Mr. Droms.Source:Jonathan Clements, “Recipe for Successful Investing: First, Mix Assets Well,”The Wall Street Journal,October 6, 1993. Reprinted by permission ofThe Wall Street Journal,169。 1993 Dow Jones amp。 Company, Inc. All rights reserved worldwide.But why stop at portfolioB?We can continue to ratchet the CAL upward until it ultimately reaches the point of tangency with the investment opportunity set. This must yield the CAL with the highest feasible rewardtovolatility ratio. Therefore, the tangency portfolio, labeledPinFigure , is the optimal risky portfolio to mix with Tbills. We can read the expected return and standard deviation of portfolioPfrom the graph inFigure :In practice, when we try to construct optimal risky portfolios from more than two risky assets, we need to rely on a spreadsheet or another puter program. The spreadsheet we present in Appendix A can be used to construct efficient portfolios of many assets. To start, however, we will demonstrate the solution of the portfolio construction problem with only two risky assets (in our example, longterm debt and equity) and a riskfree asset. In this simpler twoasset case, we can derive an explicit formula for the weights of each asset in the optimal portfolio. This will make it easier to illustrate some of the general issues pertaining to portfolio optimization.The objective is to find the weightswDandwEthat result in the highest slope of the CAL (., the weights that result in the risky portfolio with the highest rewardtovolatility ratio). Therefore, the objective is to maximize the slope of the CAL for any possible portfolio, ourobjective functionis the slope (equivalently, the Sharpe ratio)Sp:p. 208Fi