Expert Level

Learn advanced topics about trading strategies, risk management and more.

Lesson 6: How Risk/Reward Ratio Works

What is the Risk/Reward Ratio?

investors use the risk / reward ratio to equate the expected returns of the
investment with the amount of risk that they must undergo to obtain the
returns. Traders often use this approach to the decision that trades to take,
and the ratio is determined by dividing the amount that the trader is expected
to lose if the value of the asset moves in an unexpected direction (risk) by
the amount of profit that the trader expects to make when the position is
closed (the reward).

How the Risk/Reward Ratio Works

The risk /
reward ratio is often used as a metric when investing in individual stocks. The
optimal risk / reward ratio varies widely between different trading strategies.
Many test-and-error approaches are typically required to determine the ratio is
better for a given trading strategy, and many investors have a pre-specified
risk / reward ratio for their investments.

In many
situations, market strategists find that the optimal risk / reward ratio for
their investments is roughly 1:3, or three units of expected return for each
unit of additional risk. Investors can control risk / reward more explicitly
through the use of stop-loss orders and derivatives, such as options.

What does the Risk/Reward Ratio
tell you?

The risk /
reward ratio helps investors control their risk of losing business money. Even
if a trader has some profitable trades, he will lose money over time if his
winning level is below 50%. The risk / reward ratio calculates the difference
between a stop-loss entry point and a sale or take-profit order. Comparing
these two sets the ratio of gain to loss or reward to risk.

often use stop-loss orders when trading individual stocks to help minimize
losses and control their holdings directly with a risk / reward emphasis. A
stop-loss order is a trading mechanism imposed on a stock that automates the
selling of the stock from a portfolio if the stock hits a stated limit.
Investors can automatically set stop-loss orders through brokerage accounts
which usually do not entail exorbitant additional trading costs.

Example of the Risk/Reward Ratio in

this definition: a trader buys 100 shares of XYZ Company at $20 and places a
stop-loss order at $15 to ensure that losses do not reach $500. Even, say that
this trader assumes that the value of XYZ will be $30 in the next few months.
In this scenario, the trader is willing to risk $5 per share to make the
expected return of $10 per share after the closing of the position. Since the
trader is supposed to double the amount that it has lost, it would be said to
have a 1:2 risk / reward ratio for that particular trade. Derivative contracts,
such as put contracts, which give their holders the right to sell the
underlying asset at a specified price, may have a similar effect.

If a more
cautious investor is seeking a 1:5 risk / reward ratio for a given investment
(five units of expected return for each additional risk unit), then a stop-loss
ratio can be used to change the risk / reward ratio to its own requirement. In
this case, in the trading example described above, if an investor had a 1:5
risk / reward ratio required for his investment, he would set the stop-loss
order at $18 instead of $15—that is, he would be more risk-averse.

Lesson 7: Managing

In the
financial world, risk management is the method of defining, assessing and
embracing or alleviating uncertainty throughout investment decisions.
Essentially, risk management occurs when an investor or fund manager analyzes
and tries to measure the potential for investment losses, such as a moral
hazard, and then takes appropriate action (or inaction) in terms of its
investment goals and risk tolerance.

What’s Risk Management?

management is taking place everywhere in the financial world. This occurs when
an investor buys low-risk government bonds over riskier corporate bonds, when a
fund manager hedges his currency exposure to currency derivatives, and when a
bank conducts a credit check on an entity before issuing a personal line of
credit. Stock brokers use financial instruments such as options and futures,
and money managers use portfolio and asset diversification approaches to reduce
and effectively manage risk.

risk management can have serious consequences for businesses, individuals and
the economy. For example, the 2007 subprime mortgage crisis which helped cause
the Great Recession resulted from poor risk management decisions, such as
lenders that extended mortgages to low-credit individuals, investment firms
which purchased, bundled, and resold those mortgages, and funds which invested
heavily in repackaged, but still risky, mortgage-backed securities (MBSs).

The Good, the Bad, and the

We tend to
think of “risk” in mostly negative terms. In the investment world,
however, the risk is inevitable and inseparable from success.

A common
definition of investment risk is a divergence from the expected outcome. This
can be expressed in absolute terms or in relation to something like a market
benchmark. This can be positive or negative, and is linked to the concept of
“no pain, no gain” (to achieve higher returns, in the long run, you
have to consider a more short-term risk in the form of volatility).

How much
volatility depends on your risk tolerance, which is an expression of the
willingness to expect volatility based on specific financial circumstances and
the propensity to do so, considering the psychological comfort with ambiguity
and the likelihood of incurring significant short-term losses.

How Investors Measure Risk

use a variety of tactics to define threat. One of the most widely used absolute
risk metrics is a standard deviation, a numerical indicator of dispersion
around a central trend. You look at the average return on investment and then
consider the average standard deviation over the same time period. Standard
distributions (the common bell-shaped curve) indicate that the estimated return
on investment is likely to be one standard deviation from the average of 67% of
the time and two standard deviations from the average of 95% of the time. It
allows investors to quantify the risk numerically. When they feel that they can
bear the risk, both financially and emotionally, they will invest.

example, during the 15-year period from 1 August 1992 to 31 July 2007, the
average annualized total return of the S&P 500 was 10.7%. This number shows
what’s happened over the entire period, but it doesn’t tell what’s happened
along the way. The median S&P 500 standard deviation for the same period
was 13.5 percent. This is the difference between the average return and the
actual return at most points throughout the 15-year period.

applying the bell curve method, any given result should be about 67% of the
time within one standard deviation of the mean and about 95% of the time within
two standard deviations. The S&P 500 shareholder could therefore expect a
return of 10.7 percent plus or minus the standard deviation of 13.5 percent at
any given point during this period; it may also expect a 27 percent increase or
decrease of 95 percent of the time (two standard deviations). If he can afford
the loss, he’s going to invest.

Risk and Psychology

While this
knowledge may be beneficial, it does not fully address the risk issues of an
investor. The area of behavioral finance contributed to the risk equation by
explaining asymmetry between how people perceive gains and losses. In the
language of prospect theory, the area of behavioral finance pioneered by Amos
Tversky and Daniel Kahneman in 1979, investors demonstrate aversion to loss:
they put more weight on the pain of loss than on the good feeling of gain.

Also, what
investors really want to know is not just how much the asset deviates from its
expected outcome, but how bad things appear to the left-hand tail of the distribution
curve. Value at Risk (VAR) aims to provide an answer to this question. The
concept behind VAR is to measure how bad an investment loss could be with a
certain level of confidence over a defined period of time. For example, the
following statement would be an example of VAR: “With about 95 per cent
confidence, the most you can lose on this $1,000 investment over a two-year
time horizon is $200.” The confidence level is a probability statement
based on the statistical characteristics of the investment and the shape of its
distribution curve.

Of course,
even a method like VAR does not guarantee that 5% of the time is going to be
much worse. Spectacular disasters such as that of the Long-Term Capital
Management hedge fund in 1998 remind us that so-called “outlier
incidents” can occur. In the case of LTCM, the Russian government
defaulted on its unpaid sovereign debt commitments, an occurrence that
threatened to bankrupt the hedge fund, which had highly leveraged assets worth
more than $1 trillion; if it had failed, the global financial system could have

Passive vs. Active Risk

behavioral trend-oriented risk metric is a drawdown, which refers to any time
during which the return of the asset is negative compared to the previous high
point. In calculating the drawdown, we try to deal with three things: the
intensity of each negative period (how bad), the length of each negative period
(how long) and the frequency (how often).

example, in addition to wanting to know whether the S&P 500 was beaten by
the mutual fund, we also want to know how risky it was. One indicator for this
is beta (known as “market risk”), based on the statistical properties
of covariance. A beta greater than 1 indicates more risk than the market, and
vice versa.

Beta helps
us understand the principles of passive and active risk. The chart below shows
the time series of returns (each data point marked ‘+’) for a particular
portfolio R(p) versus the market return R(m). The returns are cash-adjusted, so
the point where the x axis and y axis converge is the cash-equivalent return.
Drawing the best fit line through the data points helps us to measure the
passive risk (beta) and the active threat (alpha).

gradient of the line is the alpha of the line. For example, a gradient of 1.0
means that for every unit increase in market return, the return on the
portfolio also increases by one unit. A director using a passive management
strategy may attempt to increase portfolio returns by taking more market risk
(i.e. beta greater than 1) or alternatively lower portfolio risk (and return)
by reducing portfolio beta below 1.

Influence of Other Factors

If the
rate of market or systemic uncertainty was the only factor of impact, the
return on the portfolio would always be equal to the beta-adjusted return on
the stock. This is not the case, of course, as the returns differ due to a
number of factors not linked to market risk. Investment managers who follow an
aggressive approach take additional risks to generate maximum returns on market
performance. Effective strategies include inventory, sector and country choice,
fundamental analysis and graphing.

managers are looking for an alpha, an indicator of excess return. In our
diagram example above, alpha is the sum of return of the portfolio not
described by beta, expressed as the difference between the intersection of the x-axis
and the y-axis, which can be either positive or negative. In their search for
excess returns, active managers expose investors to an alpha risk, the risk
that the result of their bets will prove negative rather than optimistic. For
example, the manager may think that the energy sector would outperform the
S&P 500 and increase the weighting of its portfolio in this sector. When
unforeseen economic conditions result in a sharp decline in energy stocks, the
director is likely to underperform the index, an example of alpha threat.

The Cost of Risk

general, the more successful the investment strategy (the more alpha the fund
manager tries to generate), the more the investor will have to pay for the
exposure to the strategy. For a strictly passive asset such as an index fund or
an exchange-traded fund (ETF), you can charge 15-20 basis points in annual
management fees, while for a high-octane hedge fund which employs complicated
trading strategies involving high capital commitments and transaction costs, an
investor would have to pay 200 basis points in annual fees, plus 20 percent of
income to the director.

disparity in pricing between passive and active strategies (or beta-risk and
alpha-risk, respectively) allows some investors to try to separate these risks
(e.g. pay lower beta-risk fees assumed and focus their more costly exposures on
specifically defined alpha-risk opportunities). This is commonly known as
portable alpha, the concept that the alpha component of the total return is
distinct from the beta component.

An example
of this would be if a fund manager claimed to have an aggressive sector
rotation strategy to beat the S&P 500 and, as evidence, reported an average
annualized beating of 1.5 percent of the index. To the investor, the 1.5% of
the excess return is the value of the director, the alpha, and the investor is
willing to pay higher fees to receive it. The remainder of the total return,
which the S&P 500 itself won, likely has nothing to do with the unique
ability of the manager. Portable alpha approaches use derivatives and other
resources to optimize how the alpha and beta elements of their distribution are
obtained and paid for.

The Bottom Line

Risk is inseparable from
return. Each investment entails some degree of risk, which may be very close to
zero in the case of the U.S. Treasury protection or very strong for such issues
as concentrated exposure to Sri Lankan equities or real estate in Argentina.
Risk is quantifiable in both absolute and relative terms. A solid understanding
of risk in its different forms can help investors to better understand the opportunities,
trade-offs, and costs involved with different investment approaches.