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## C HAPTER 11

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**CHAPTER11**Diversification and Risky Asset Allocation Chapter Sections: Expected Returns and Variances Portfolios Diversification and Portfolio Risk Correlation and Diversification The Markowitz Efficient Frontier**Diversification**• Diversification • Spreading your investments across a number of asset classes to eliminate some, but not all, of the risks of investing • “Don’t put all your eggs in one basket” • Old, old saying … as opposed to … • “Put all your eggs in one basket … And Watch That Basket!” • Mark Twain (maybe erroneously attributed)**Diversification**(continued) Diversification has been one of the best methods to reduce risk**But How Do You Measure Risk?**• We Have Come Full Circle! • Way back in Chapter 1, we introduced the tug-of-war between risk and return • We saw how the higher the average annual return, the higher the standard deviation (and its companion measure variance) from the average annual return • We have studied the major financial asset classes • Mutual funds, stocks, bonds, “cash” • We discussed the risks and returns of each • Return is easy to measure • How much money did you make? How long did it take? • Risk is very difficult to measure • It is even harder to anticipate – Witness 2008!**Variance & Standard Deviation**• Variance and its more useful companion, standard deviation, tell us how much an asset class will vary from the expected return • These measures are readily available from the investment community • And da’ numbers ain’t pretty… • For any randomly selected stock on the NYSE, the standard deviation is 49.24%! • That means in any one year, many stocks on the NYSE – the most stable stocks! – will vary up or down close to 50% from their annual average return • So how can we reduce the variance? In other words, how can we reduce the risk?**Variance & Standard Deviation**(continued) • The answer, of course, is to diversify! • If we go from 1 randomly selected stock to 2 randomly selected stocks, • The standard deviation goes from 49.24% down to 37.36% • If we randomly select 10 stocks, • The standard deviation goes down to 23.93% • 20 stocks, • 21.68% • And so on… Diversifying our stock portfolio reduces our risk substantially (as measured by reduced variance and standard deviation)**Variance & Standard Deviation**(continued)**Variance & Standard Deviation**(continued) But there is a limit to which diversification can reduce your risk in any given asset class (in this case, stocks). Why? “Correlation.”**Correlation**• Correlation • The tendency of the returns of two assets to move together • Imperfect correlation is the key reason why diversification reduces portfolio risk as measured by the portfolio standard deviation • No two investment returns will be exactly the same • Positively correlated assets tend to move up and down together • Negatively correlated assets tend to move in opposite directions**Correlation**(continued) • Correlation coefficient • The measure of how closely returns on assets move together • The correlation coefficient ranges from:**Correlation**(continued)**Correlation**(continued) • So how does this answer our question about why diversification can only reduce by so much the risks of owning stocks? • Although stocks are not perfectly correlated, • They are positively correlated enough so that stocks in general tend to move in the same direction • This is why we often refer to stock investments as a whole as the stock market • Even though at any given time, some companies are doing well, others are doing poorly, and many are simply chugging along as they always have done**Correlation**(continued) • “Darned! That is still too much risk for me! Think I’se gonna’ stick to bonds…” • You are a very conservative, risk-averse investor & you don’t like the volatility of stocks • Therefore, you decide to place all your investments into bonds • You will accept the lower return from the bonds in exchange for the lower risk of the bonds • Oops! Bad idea! Why? Because, like stocks, • Bonds are positively correlated with themselves • They also will tend to do well & do poorly as a whole • And they are often negatively correlated with stocks! • Stocks & bonds often (but not always) move in opposite directions**Correlation**(continued)**Correlation**(continued)**Correlation and Diversification**(continued) • A combination of stocks and bonds actually created a portfolio with less risk • While earning you more return than just bonds • If you are seeking less risk, it not only pays to diversify within an asset class, • It pays to diversify among asset classes • The same kind of relationship occurs with domestic and foreign stocks and bonds (although less now than in the past) • Although diversification is still not a guarantee of positive results • No diversification scheme worked well in 2008! • We have a name for choosing the appropriate mix for an investor • It is called …**Asset Allocation**• Fancy term for… • “How much should I have in stocks? How much in bonds? How much of each stock & bond type?” • Many advisors suggest a formula such as… • Subtract your age from 100 (or 110 or 120) • That is the percentage of stocks you should own • The rest should be in bonds • Example: A 40-year-old would have 100-40 or 60% invested in stocks and 40% in bonds • “Poppy-cock!” say others (myself included) • Buy high-quality stocks and put up with the risk • Once you near retirement, start buying bonds**Asset Allocation**(continued) • Example: $100,000 –How do I divvy it up? • $25,000 Bonds • $15,000 High grade corporate & government • $5,000 High yield (a.k.a. junk) bonds • $5,000 Global bonds • $75,000 Stocks • $25,000 Domestic growth and income • $25,000 Global growth and income • $10,000 Aggressive growth • $10,000 International • $5,000 Small company stocks**Rebalancing**• Some of those same advisors that suggest asset allocation also suggest the technique of rebalancing • Every year, check to see if your percentages are still in balance • If stocks have had a banner year, you might now be at 70/30 instead of your target 60/40 allocation • Sell enough stocks and buy enough bonds to bring the balance back to your target 60/40 allocation • Likewise, if stocks have tanked, sell bonds & buy stocks to bring the percentage back up to 60/40 • Forces you to “Do the right thing” • “Buy Low, Sell High”**Stocks & Bonds in Retirement**• Many advisors suggest that retirees shed the bulk of their stock investments in favor of bonds and cash investments • The only problem is… • People are living much, much longer • A 50-year-old living today has a 50/50 chance of living to see 100 years old! • As you near retirement, start migrating your investments from stocks to bonds • But don’t abandon stocks entirely! • See ICA Illustration, Bonds versus Stocks**Dollar Cost Averaging**• A system of buying an investment at regular intervals with a fixed dollar amount • With Dollar-Cost Averaging, there is always “Good News” • “The market is up! Good News!” • Your account is worth more • “The market is down! Good News!” • Next month, you will get more shares at a lower price when the $50 or $100 comes out of your paycheck or checking account Yippee! Huh?!**Dollar Cost Averaging Example**(continued) In this example, your average cost per share is $6.92 ($3,000 / 433.333 shares). But the price per share is $7.50. So although it looks like you should have simply broken even, you actually made money because you bought more shares at the lower prices. The value of the shares is $3,250 (433.333 * $7.50).**Dollar Cost Averaging**(continued) • By always investing the same amount of money, you are purchasing more shares when the price is low and fewer shares when the price is high • Your average cost per share should be lower than your average price per share • However, it is not a guarantee of success • Dollar cost averaging is not going to help a lousy investment turn a handsome profit! • But it does makes investing very, very easy • For mutual fund investors, that is • It is a bit trickier with stocks & bonds • But not impossible**Mutual Funds & Diversification**• Speaking of Mutual Funds • Wasn’t diversification one of the two main reasons why so many investors choose mutual funds? Yes! • (The other is professional money management) • But does that mean mutual funds necessarily have less risk than individual portfolios? • Well, it all depends on which mutual funds we are talking about… For examples, go to morningstar.com or finance.yahoo.com, enter a mutual fund such as AIVSX and find the link to [Risk]. Try some other mutual funds. Let’s look at some examples…**CHAPTER11 – REVIEW**Diversification and Risky Asset Allocation Chapter Sections: Expected Returns and Variances Portfolios Diversification and Portfolio Risk Correlation and Diversification The Markowitz Efficient Frontier Next week: Chapter 15, Stock Options