Risk-adjusted Return
Michael Tove Ph.D, CEP, RFC
January 2015
Of all the messages that investors get from their investment advisors, the biggest myth they
perpetuate is that an investor will increase return by increasing risk. To be sure, everyone likes
growth and given all other thing things equal, who wouldn’t seek higher return than lower? This
financial goal has been the source of numerous theories on investing and portfolio
diversification. Nobel Prizes in Economics have been awarded to theoreticians for devising
models of how to “beat the stock market.”
Unfortunately, theory and practice are often not the same. Investors commonly swear they’ve
beaten the markets, and in some cases, it may be true. But more often than not, they’re fooling
themselves. This was never more true than the first decade of the 21st Century which experienced
two of the country’s biggest market corrections.
Lately, a growing body of research has taken sharp exception with traditional investment models.
For example, research by Morningstar (2006, Kinnel 2014, see also Herring et al. 2010, Jaffe
2014, Kitces, 2012, etc.) demonstrated that investors, seldom if ever achieve the full potential
they expect. For example, according to Russel Kinnel, Morningstar’s director of mutual funds
research, from 2003-2013, investors averaged 2.5% poorer return than the market, gaining on
average 4.8% per year compared with 7.3% per year for a typical mutual fund. Where investors
did the worst was trying to time the markets; buying and selling in an attempt to “buy low and
sell high” which, theoretically, is the only way to “beat” the market.
These are not merely “opinions” but conclusions supported by research data and scientific
analysis and their conclusions are not wrong. In short, the central message is that risk is not only
very real, but the primary reason for investment portfolio failure and the only way to reduce the
harm caused by market risk to reduce the risk itself.
Sadly, few investment advisors (or individual investors for that matter) have the background,
training, or time to analyze investment risk for typical investment portfolios. Even if they did,
they would likely find it even more challenging to explain to the majority of investors, what it
meant in a meaningful way. It’s the reason why the vast majority of investment advisors don’t do
it – but they should. Lack of appreciation for the potential harm that risk poses is why investors
fail to meet their financial objectives. The cliché expression “what you don’t know can’t hurt
you” does NOT apply to investing.
But measuring and assessing risk doesn’t have to be that complex. This paper will offer a
simplified way to understand risk and assist average investors reach better and more reliable
choices in building and balancing a successful portfolio.
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WHAT IS RISK-ADJUSTED RETURN?
Another reason “higher risk yields higher return” is false is that theoretical (meaning historical)
return is not the same as future or expected return. Hindsight is a wonderful thing and everybody
would have amazing returns if only by the use of hindsight. Ironically, the investment industry’s
regulatory entities, the U.S. Securities and Exchange Commission (SEC) and the Financial
Industry Regulatory Authority (FINRA) have long admonished that “Past performance is not a
guarantee of future returns.” It’s so common, it’s cliché but at the end of the day, too few
investors actually give that cautionary note the consideration it deserves. Everyone talks about
“Return” when they should be talking about “Risk-adjusted Return.”
There are two components to return.
Possibility – Or the expected level of return, often expressed as a percent yield per year. This
applies to both capital appreciation (growth in investment value) and dividend payments.
Fundamentally, either a return is guaranteed or it isn’t. Any return that’s not guaranteed with
absolute certainty is a “Possible Return.”
Probability – Or the statistical chance of achieving the expected (possible) return. It is the
component to which the caveat “Past performance…” refers. Probability is risk.
Since the 1960’s a number of prominent economists have cautioned that it’s wrong to look only
at expected return (Possibility) without giving equal consideration to risk (Probability). Nobel
Laureate William Sharpe and colleagues (Litner 1965, Mossin 1966, Sharpe 1964, Traynor 1961,
1962) gave us the Capital Asset Pricing Model and the Sharpe Ratio (Sharpe 1994), a
mathematical models which measures portfolio return against portfolio standard deviation (σ) as
a measure of risk. Jack L. Traynor (1961, 1962) offered a similar formula that uses portfolio beta
(β) as a measure of risk. Other models exist but the bottom line is all these formulae seek to
represent expected return in light of risk.
Unfortunately, few investment advisors give much consideration to these fundamental concepts
and fewer still actually do the math before making specific portfolio recommendations. And,
those few that do, cannot easily translate what the resulting numbers mean to investors in easyto-understand terms. However, the concepts need not require complex mathematical equations or
advanced degrees to understand what the results mean.
Consider the following:
Assume your bank offers a one-year CD promising 2% interest for 12 months. The Possibility of
return is 2% and the Probability of achieving that return is 100% (or in decimal form = 1.0). In
other words, because the return is guaranteed, there is no risk of not achieving it. So far so good,
right? So if we multiply the two. In other words, the risk-adjusted return equals the Possible
Return times the Probability of Success, thus 2.0% X 100% = 2.0%. Technically, this is the
definition of “Guaranteed Return.”
Let’s now go to the opposite extreme: the Lottery (don’t laugh). Let’s assume you buy a $5
Lottery ticket and the jackpot is $50 Million. If you win, your return (Possibility) would be 1
Billion percent; assuredly a lot better than that lousy 2% from the bank. But there’s a catch. The
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Probability of success is infinitesimally small. In fact, for all practical purposes, it’s 0.
Therefore, Possibility (1,000,000,000%) X Probability (0%) = 0%.
In other words, just because an expected return is possible does not mean it will occur or is even
likely to occur.
Let’s take this one step further. Suppose there’s an investment with a 10% expected annual
return (Possibility) and a risk of 50% (Probability). Every other year you will not get what you
expect. In other words, it’s a coin toss. You toss your coin and it comes up heads, you get 10%.
You toss the coin and it comes up tails, you get nothing. Over the course of years, you will net
5% (10% Possibility X 50% Probability = 5%) That’s the risk-adjusted return.
When comparing two investment possibilities, this simple concept should be what guides your
choices.
For example, assume Investment A has an expected average annual (compound) return of 10%
and a risk of 40% meaning a 4 in 10 chance of NOT achieving the expected return. Translated,
that means the Probability of Success is 60%.
In contrast, Investment B has an expected return of 8% but a risk of 10% (Success Probability =
90%)
Compare the two:
Return
Success
Risk-adjusted
Possibility Probability
Return
Investment A
10%
60%
6.0%
Investment B:
8%
90%
7.2%
Given all other things equal, Investment B is obviously the smarter choice.
When considering portfolio diversification, the impact of risk-reduction (Probability) can be far
greater than the impact of expected return (Possibility). The conclusion from that is that net
return can be increased not by chasing more and more risky investments in the hope of realizing
Possibility but by reducing portfolio risk and thereby increasing the likelihood (Probability) of
actually achieving the expected result.
MORE ABOUT RISK.
Several factors impact risk:

Volatility – This refers to the swings from high to low in how a particular investment
performs. Often measured as the Standard Deviation, this is simply a statement of the range
of expected possible returns. Thus, an investment that averaged 10% whose best year was
15% and worst was 5% has a much lower Standard Deviation (risk) than an investment that
averaged 10% whose best year was 50% and worst year was -30%.
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
Time Horizons – Within a single investment choice, the longer a person’s time horizon, the
less the risk. This relates back to Standard Deviation again because an investment which has
big swings in performance from high to low will be far more likely to “average out” over a
long time than a short time when the investor might be very lucky or very unlucky (the
operative term here being “lucky” which takes us back to the lottery example, earlier).
Of critical importance, however, in assessing one’s Time Horizon, is an understanding what
that term really means. With regard to risk, a time horizon is the time (in years) between
today and the first withdrawal of funds from the account. Your current Time Horizon gives
no credit for years past.
Exhaustive research (for a review, see Greene 2013, Voegtlin and Pfau 2014) has shown that
withdrawing even as little as 4% of the portfolio’s value per year carries a 57% chance of
depleting the portfolio to $0. This simple, yet surprising finding is especially relevant when
retirees reach their “Required Beginning Age” on mandatory withdrawals from their IRA and
401(k) plans. IRS rules require that (with rare exception) these pre-tax dollar retirement plans
be liquidated starting at age 70½. The schedule of mandatory distributions starts at a little
less than 4% per year and rises annually. Once these mandatory distributions begin, the
investor’s time horizon is 1 year – woefully short (and too risky) for an investment portfolio
for anyone, especially a 70-year old.

Diversification – This is another cliché term that everyone knows but few truly understand.
In theory diversification means having a bunch of different investments with different
objectives. In practice, it means having different investments which do NOT correlate with
each other, meaning move at different rates and in different directions. Sadly, few
investments behave as differently from each other as is commonly believed. In part, this is
because in today’s electronically linked global economy, investors react to short-term
financial news with little regard to the long-term financial status of the companies in which
they are invested. It’s what Nobel Laureate and Yale University’s Sterling Professor of
Economics, Robert Shiller (2000, 2005), calls “Irrational Exuberance.” Thus, when markets
react to good or bad news, corporate stocks on the whole often move up or down in unison
simply because of the news. This is the “irrational” component. Shiller (e.g., in course
lectures on Economics at Yale) has further demonstrated that these “movements” of markets
relate more to random events than to predictable patterns. For the investor, it means that
despite popular belief, “diversifying a portfolio” by owning many different investments,
especially if all mutual funds (which are each a collection of investments), may offer no true
advantage over simply owning one basic mutual fund.
Owning two investments which move in the same direction by comparable amounts and the
same time are duplicative, not diversified. The truth is most investment portfolios, especially
those constructed by computer models, are over-diversified meaning they contain more
investment choices than are necessary. Over-diversification adds complexity and cost for no
comparable benefit. Essentially, the only way to correctly diversify a portfolio is by owning a
mix of different financial products which do not respond to the same economic pressures in
the same way or at the same time.
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
Personal risk tolerance – Not everyone is the same and a single investment portfolio that is
too conservative for one person may be too aggressive for another.
o Age. A particular investment portfolio that is very suitable for a 35 year-old might be
completely unsuitable for a 65 year-old.
o Knowledge and expertise. The less an investor knows about how investments work,
what the specific risks, expectations – possibilities – are, etc. the less risk they should
accept.
o Comfort Level. A person who feels nervous about loss should not have the same
portfolio as someone who has little or no concern about that.
o Income and liquidity. The more income, net worth and available cash not at risk a
person has, the more investment risk they can tolerate with the rest of their portfolio.
CONCLUSION.
Building financial portfolios around Risk-adjusted Return is better than using “return.” Doing so
requires considering both potential return and possible risk equally and building the portfolio
from there. Although the calculations are relatively easy to do, they should still be done by
knowledgeable professionals.
REFERENCES:
Greene, Kelly. 2013. Say Goodbye to the 4% Rule. The Wall Street Journal.com. March 3.
http://www.wsj.com/articles/SB10001424127887324162304578304491492559684
Herring, Richard, Francis X. Diebold, and Neil A. Doherty. 2010. The Known, the Unknown, and
the Unknowable in Financial Risk Management: Measurement and Theory Advancing Practice.
Princeton, N.J: Princeton University Press.
Kinnel, Russel. 2014. Mind the gap 2014. Morningstar Fund Investor, Online report, February
27.
Kitces, Michael. 2012. Does the DALBAR study grossly overstate the behavior gap? Nerd’s Eye
View, Kitces.com, October 3. https://www.kitces.com/blog/does-the-dalbar-study-grosslyoverstate-the-behavior-gap-guest-post/
Jaffe, Chuck. 2014. Mutual funds far out-perform mutual fund investors. MarketWatch, Inc.
Online report, March 5. http://www.marketwatch.com/story/mutual-funds-are-smarter-than-you2014-03-04
Lintner, John. 1965. The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13–37.
http://efinance.org.cn/cn/fm/The%20Valuation%20of%20Risk%20Assets%20and%20the%20Sel
ection%20of%20Risky%20Investments%20in%20Stock%20Portfolios%20and%20Capital%20b
udgets.pdf
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Morningstar, Inc. 2006. Fact Sheet: Morningstar Investor Return.
Mossin, Jan. 1966. Equilibrium in a Capital Asset Market. Econometrica, Vol. 34, No. 4, pp.
768–783.
http://efinance.org.cn/cn/fm/Equilibrium%20in%20a%20Capital%20Asset%20Market.pdf
Sharpe, William F. 1994. The Sharpe Ratio. The Journal of Portfolio Management 21(1): 49–58.
http://web.stanford.edu/~wfsharpe/art/sr/sr.htm
Shiller, Robert J. 2000. Irrational Exuberance. Princeton University Press.
Shiller, Robert J. 2005. Irrational Exuberance, Second Edition (revised). Princeton University
Press.
Treynor, Jack L. 1961. Market Value, Time, and Risk. Unpublished manuscript.
Treynor, Jack L. 1962. Toward a Theory of Market Value of Risky Assets. Unpublished
manuscript. A final version was published in 1999, in Asset Pricing and Portfolio Performance:
Models, Strategy and Performance Metrics. Robert A. Korajczyk (editor) London: Risk Books,
pp. 15–22.
Voegtlin, Rex and Wade D. Pfau. 2014. Mitigating the Four Major Risks of Sustainable
Inflation-Adjusted Retirement Income. A White Paper by the Annexus Research Institute.
https://www.immediateannuities.com/pdfs/articles/mitigating-the-four-major-risks-ofsustainable-inflation-adjusted-retirement-income.pdf
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