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CHAPTER 11Diversification and Risky Asset Allocation

Chapter Sections:Expected Returns and VariancesPortfoliosDiversification and Portfolio RiskCorrelation and DiversificationThe Markowitz Efficient Frontier

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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)

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Diversification

Diversification has been one of the best methods

to reduce risk

(continued)

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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!

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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

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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…

Variance & Standard Deviation(continued)

Diversifying our stock portfolio reduces our risk substantially (as measured by reduced variance and standard deviation)

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Variance & Standard Deviation(continued)

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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.”

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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

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Correlation coefficient The measure of how closely returns on assets

move together The correlation coefficient ranges from:

(continued)

From: -1 (perfect negative correlation)

through: 0 (uncorrelated)

To: +1 (perfect positive correlation)

Correlation

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(continued)Correlation

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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

(continued)Correlation

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“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

(continued)Correlation

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(continued)Correlation

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(continued)Correlation

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A combination of stocks and bonds actually created a portfolio with less riskWhile 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 classesThe 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 investorIt is called …

(continued)Correlation and Diversification

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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 ownThe 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

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Asset Allocation 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

(continued)

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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”

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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

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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?!

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Dollar Cost Averaging Example

YearYou

Invest

Share

Price

Shares

Purchased

Cumulative

Shares

1 $1,000 $10.00 100.000 100.000

2 $1,000 $5.00 200.000 300.000

3 $1,000 $7.50 133.333 433.333

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).

(continued)

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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

(continued)Dollar Cost Averaging

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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…

Let’s look at some examples…

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.

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Mutual Funds & Concentration

Many market historians have observed the tendency of mutual fund inflows and outflows to be a fairly reliable contrarian indicator of market performance.

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CHAPTER 11 – REVIEW

Diversification and Risky Asset Allocation

Next week: Chapter 15, Stock Options

Chapter Sections:Expected Returns and VariancesPortfoliosDiversification and Portfolio RiskCorrelation and DiversificationThe Markowitz Efficient Frontier