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Learning Module 4 Backtesting and Simulation 556
Exhibit 15: Sharpe Ratio for BM and RP Portfolios in Different Macro
Scenarios (1993–2019)
Sharpe Ratio
A. Economic Scenarios
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
0.5 0.5
0
Recession Recession Non-Recession Non-Recession
Benchmark Risk Parity
Sharpe Ratio
B. Market Volatility Scenarios
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
0.5 0.5
0
High–Vol Regime High–Vol Regime Low–Vol Regime Low–Vol Regime
Benchmark Risk Parity
Sources: Bloomberg Finance LLP, FTSE Russell, S&P Capital IQ, Thomson Reuters, Wolfe Research
Luo’s QES.
In addition to the Sharpe ratio, a probability density plot can reveal additional informa-
tion about the sensitivity of the return distributions of these investment strategies—for
example, during recession versus non-recession periods. As shown in Exhibit 16, the
distribution of returns for both the BM and RP strategies is flatter in a non-recession
environment, which implies higher standard deviations during these regimes. The
BM strategy suffers from negative skewness and excess kurtosis (i.e., fat tails to the
left), regardless of the recession regime, but its average return is clearly lower in a
recession environment (Panel A). The RP strategy also has a lower average return in
the recession regime (Panel B), but its volatility and kurtosis are both also much lower
compared with those of the BM strategy.
© CFA Institute. For candidate use only. Not for distribution.

Simulation Analysis 557
Exhibit 16: Distribution of Returns for Factor Allocation Strategies:
Recession and Non-Recession Regimes
0
0
Density
A. Benchmark
50 50
40 40
30 30
20 20
10 10
0
–0.14 –0.14 –0.02 –0.02 –0.10 –0.10 –0.06 –0.06 0.06 0.06 0.02 0.02
Monthly Return
Density
B. Risk Parity
80 80
60 60
40 40
20 20
0
–0.04 –0.04 –0.02 –0.02 0.04 0.04 0.02 0.02
Monthly Return
Recession Regime Non-Recession Regime
Sources: Bloomberg Finance LLP, FTSE Russell, S&P Capital IQ, Thomson Reuters, Wolfe Research
Luo’s QES.
SIMULATION ANALYSIS
contrast Monte Carlo and historical simulation approaches
explain inputs and decisions in simulation and interpret a simulation;
and
In backtesting, we essentially assume that we can go back in time, apply our invest-
ment strategies, rebalance our portfolio(s), and measure performance. This idea is
intuitive because it mimics how investing is done in reality—that is, forming our
ideas, implementing our strategies, and incorporating new information as it arrives.
7
© CFA Institute. For candidate use only. Not for distribution.

Learning Module 4 Backtesting and Simulation 558
Backtesting implicitly assumes that the past is likely to repeat itself, however, and
this assumption does not fully account for the dynamic nature of financial markets,
which may include extreme upside and downside risks that have never occurred before.
We now explore how simulation can provide a more complete picture.
There are two basic types of simulation: historical and Monte Carlo. In histori-
cal simulation , rather than assuming we implemented a strategy at some past date
and collecting results as the strategy runs over time, we instead construct results by
selecting returns at random from many different historical periods (windows) without
regard to time-ordering. Although this approach does assume, like rolling-window
backtesting, that past asset returns provide guidance about future asset returns, it
relaxes a key restriction by randomly changing the sequencing of historical periods
from which factor returns are drawn. As a result, historical simulation is essentially