Investments can growth wealth two ways: by returning income to you and by growing in value. *Expected return* is the combination of income and growth you expect on an investment in a single year. Of course investments can also fluctuate in value, and some fluctuate more than others. Investment professionals call that fluctuation *volatility*. The wider the fluctuations, the higher the volatility.

Ideally you would like your investments to have as high an expected return as possible. Unfortunately, the price of high expected returns is high volatility. Portfolio math helps investment professionals balance the trade-off between expected return and volatility.

One of the best ways to help your assets grow is to lower the volatility as much as possible without losing expected return. That is where diversification comes in.

Imagine you could invest in three investments, each with the same expected return, 8%. One investment is a diversified portfolio, with volatility of 15%. The second investment is a single asset class, with volatility of 25%. The third is a single stock, with volatility of 40%.

Figure 1 depicts what seven-years of returns could look like for these three investments^{[1]}.

*Returns depicted are hypothetical, for purposes of illustration only*

[1] For all three we assume the same expected annual log return of 8%. Volatilities listed in the article are log volatilities.

These volatility levels are reasonable approximations for a diversified investment portfolio (at 15%), a single asset class (at 25%), and a single stock (at 40%). Notice the 15% volatility series fluctuates the least, and the 40% volatility series fluctuates the most. It has more extreme ups and downs. Its extreme negative returns destroy wealth, because it is so hard to recover from them.

Figure 2 plots Growth of $100 based on the returns depicted in Figure 1.

*Returns depicted are hypothetical, for purposes of illustration only*

As you can see, for the Single Stock the extreme negative returns in down years destroyed its owner’s wealth. This is not a strategy a retirement saver can plan on.

In the following charts, you will see that if you invest in a strategy that has higher volatility, like the single stock strategy, you will have a greater chance of winding up with lower wealth because of the likelihood of bad outcomes.

Figures 3, 4, and 5 depict 1,000 simulations of the same three investments depicted in Figures 1 and 2. The diversified portfolio has volatility of 15%, the single asset class has volatility of 25%, and the undiversified portfolio has volatility of 40% (akin to that of a single stock).

*Returns depicted are hypothetical, for purposes of illustration only*

In Figure 3, 90% of the results are within the range of $91 to $285, with a median of $159. Over 90% of the results are higher than the starting value of $100, and half the results are between $124 and $204. This means if you had invested in this portfolio without making additional contributions, after seven years, your final wealth would probably have been between $91 and $284, with the most likely result $159.

Figure 4 depicts the parallel simulations for a single asset class with the same expected return.

*Returns depicted are hypothetical, for purposes of illustration only*

In Figure 4, 90% of the results are within the range of $56 to $368, with a median of $141. Over 72% of the results are higher than the starting value of $100 , and half the results are between $94 and $212. This means if you had invested in this strategy without making additional contributions, after seven years, your final wealth would probably have been between $56 and $368, with the most likely result $141. .

Figure 5 depicts the single stock simulation.

*Returns depicted are hypothetical, for purposes of illustration only*

In the single stock simulations, 90% of the results are within the range of $25 to $482, with a median of only $108. Only 52% of the results are higher than the starting value of $100 , and half the results are between $57 and $204. This means if you had invested in this strategy without making additional contributions, after seven years, your final wealth would probably have been between $25 and $482, with the most likely result only $108, a mere 8% higher than what you invested originally. This does not seem like a strategy on which you can reliably plan.

If you are saving for retirement, although you cannot know the future, if you have at least an idea of how you can expect your investments to grow you can make plans for the future. Along the way, if necessary, you can adjust your plan. But if you don’t diversify, you may wind up with something like Figure 5, which we think of less as an investment strategy and more as a gambling strategy.

Invest your retirement savings, don’t gamble!