September 2016
Win by Not Losing Investment Mathematics
The primary objective of investing for most people is the return they make on their investments. The second objective
tends to be to find investments that offer the promise of high returns with little or no risk. Of course, high returns and
low risk are typically not congruous. Therefore, in reality, investors typically seek investments that first fall within their
acceptable level of risk of loss of capital, then those investments which offer the highest return available within the
defined risk parameters.
Save speculators, most investors find the prospect of outright loss of capital generally unacceptable. Yet many investors
are willing to risk limited and temporary declines in the value of their investments if the longer term investment thesis
remains intact. The acceptable magnitude of temporary declines is unique to each investor. Thus the investment
portfolio for each investor should reflect the unique tolerance for not only potential loss of capital but also the amount
of portfolio decline they can tolerate without abandoning their overall investment strategy.
Once an investor has defined their appropriate risk and volatility parameters the job becomes to execute an investment
strategy which is aligned with such parameters and offers strong risk tempered return potential. For us, this is where the
mathematics of a "win by not losing" strategy become so compelling.
To best articulate the pure mathematical significance of an investment strategy designed to enhance the potential for
strong risk-adjusted returns we will address three key principles which we believe can contribute to achieving strong
investment returns over time. One, the power of compound growth. Two, the importance of avoiding large losses. And
three, the downside volatility penalty.
The Power of Compound Growth
At Sapient we often reference Albert Einstein's assertion that compound interest is the eighth wonder of the world.
Continual growth on growth is a truly magical phenomenon. To illustrate, consider the following scenario. If we were to
ask you if you would prefer to have $1 million dollars today or one penny that will double in value every day for the next
thirty days…which would you choose? Research indicates that most people choose the $1 million dollars today.
Unfortunately, they would consequently miss a huge opportunity. As the table below indicates, a single penny that
doubles every day for 30 days will net you more than $5 million in the end. While doubling your money every day is not
a realistic example, it does illustrate how powerful
A Penny Doubled Every Day for 30 Days
compounding is over time. Notice that the penny
Day
Value
Day
Value
had only grown to $163.84 in the first 15 days but
then grew to $5,368,709.12 in the next 15 days.
1
$
0.01
16 $
327.68
Over time the growth of the original amount and
2
$
0.02
17 $
655.36
the growth on the growth becomes a mathematical
3
$
0.04
18 $
1,310.72
wonder.
4
$
0.08
19 $
2,621.44
As this example indicates, early and consistent
5
$
0.16
20 $
5,242.88
compounding can lead to better long term results
6
$
0.32
21 $
10,485.76
for investors. On the other hand, delayed and or
7
$
0.64
22 $
20,971.52
inconsistent compounded returns can lead to less
8
$
1.28
23 $
41,943.04
attractive long term results. Any decline in portfolio
9
$
2.56
24 $
83,886.08
value, for instance, would cause a new lower
10 $
5.12
25 $
167,772.16
starting level to be established and compounding is
11 $
10.24
26 $
335,544.32
adversely affected. Thus, consistency of positive
12 $
20.48
27 $
671,088.64
returns is an important factor in maximizing
compounding, one we will address further later in
13 $
40.96
28 $
1,342,177.28
this piece.
14 $
81.92
29 $
2,684,354.56
15 $
163.84
30 $
5,368,709.12
Avoiding Large Losses
Large losses, even if they are temporary, are damaging to longer term investment returns. One major portfolio decline,
or outright loss, can undo years of successful investment returns. Limiting the downside capture of an investment is an
essential element in optimizing the benefits of compounding. As losses become larger, the gain necessary to recoup the
loss increases exponentially. For example, from 2000 to 2002 the S&P 500 Index declined 49% and a subsequent gain of
nearly 100% was required to recover the loss. From 2007-2009, the S&P 500 fell 57%, the gain required to get back to
breakeven was nearly 150%.
We believe too much emphasis is placed on beating the market on the upside. Or, in other words, striving to achieve
higher returns than the market when the market is rising as opposed to limiting losses when the market is declining. It
often comes as a surprise to investors that for the last 50 years capturing 69% of the gains in the market is all that is
required to match the overall market return if you limit losses to 60% of the market declines. Foregoing some upside
capture of returns in exchange for reducing some downside capture of losses also smooths out portfolio volatility thus
potentially lessening investor anxiety.
Another example of the importance of avoiding large losses is evident in the following scenario. If an investor were to
invest $100,000 in the Dow Jones Industrial Average at the beginning of 1950 and never touch it through the end of
2014, the $100,000 would have grown to $8,905,746. If the same investor missed the 10 best quarters out of the 256
quarters in total, the $100,000 would have grown to $1,747,070. However, if this investor had missed the 10 worst
quarters, the $100,000 would have grown to $63,401,395. Finally, if this same investor missed all of the 10 best and
worst quarters, the $100,000 would have grown to more than $12,400,000 or 40% higher than just buying and holding. 1
Thus missing or reducing the negative impact of the worst quarters had a much greater impact than missing out on the
full benefit of the best quarters.
The Downside Volatility Penalty
Just as large investment losses can impair the power of compounding, smaller and more frequent downside portfolio
volatility also undermines compound growth potential. Since 1928 the Dow Jones Industrial Average has produced an
"average” annual return of approximately 9.5%. However, the Dow's actual return has often been far greater or less
than 9.5% in any given year. As a matter of fact, the Dow only returned in the 9-10% range twice in the last 87 years.
And, only four times has the Dow returned between 7.5-11.5% in this time frame. Most of the time the Dow's return in
any given year was much greater or less than the 9.5% average. 2 This illustrates how averages can be deceptive when it
comes to measuring investment returns. Compounded or cumulative return measurements provide more precise
metrics than average return because the sequence of the returns is accurately captured not smoothed away by
averaging.
1 2
& Source: Swan Global Investments, “Math Matters: Rethinking Investment Returns & How Math Impacts Results”
The table above further illustrates the point that two investment strategies with the same average return over 5 years
can have dramatically different results where it matters most, the compounded/cumulative rate of return and the total
value of the investment at the end of the period.
As you can see, both portfolios have the same average return of 7% but the portfolio with the higher downside volatility
(Portfolio B) has the lower compound/cumulative return. This outcome is a result of negative compounding on the more
volatile portfolio. Thus lowering volatility is essential to achieving higher compound growth over time.
The table below further illustrates the impact of negative compounding when a portfolio experiences increasing levels of
volatility.
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario 6
Arithmetic Annual
Return
10%
10%
10%
10%
10%
10%
Standard Deviation
(Volatility)
0%
10%
20%
30%
40%
50%
Geometric Annual
Return
10%
9.60%
8.30%
6.03%
2.58%
-2.42%
Starting Funds
$100,000
$100,000
$100,000
$100,000
$100,000
$100,000
Ending Funds
$259,375
$250,156
$221,935
$179,629
$129,073
$78,278
Total 10 Year
Return
159%
150%
122%
80%
29%
-22%
* Source: Tyton Capital Advisors, "Low Charges and High Volatility: How to Erase Your Returns"
In summary, once an investor has determined their own personal investment objectives and reconciled them with their
unique tolerance for capital loss and volatility, it is important to understand the mathematics of investment returns in
order to optimize results. As discussed above three key elements should be considered when arriving at an investment
strategy. First, compound growth is a powerful ally. Second, avoiding large losses is critical. And third, high
investment/portfolio volatility is a detractor to returns.
Investment mathematics do matter and we believe more investors would be wise to consider a "win by not losing"
approach, which incorporates these powerful concepts, in order to attain their investment objectives.
The information and views contained in this commentary are for informational purposes only and does not constitute, and should not be construed as, investment
advice or recommendation with respect to the information or specific securities represented. All investments involve risk, including possible loss of principal. There
may be greater risks involved when investing in emerging markets. While information contained herein has been obtained from sources believed reliable, we do not
represent that it is accurate or complete, and it should not be relied upon as such. Past performance is no guarantee of future results.