1.
Sharpe has been vice-Chairman of North American of the Trilateral
2.
I recall that Gilmore’s first year coupled with his arriving just before classes started led him to use his predecessor’s (Malcolm Sharpe) outdated casebook and going along with the outmoded 3- 3- 2-credit hours regimen ending in a single three-hour exam for the whole enchilada, i
3.
One vanguard slave leader, Sam Sharpe, put this excitement into action in 1831 and organized a large passive-resistance effort against plantation owners
4.
‘’Major, we have the weapons and ammunition sent by train from the Sharpe Arsenal, along with six instructors that will teach our personnel about our new individual weapons
5.
Wickland’s attention was suddenly focused on the story at the mention of the Sharpe family, one of the more illustrious and established names in the city
6.
He seemed to recall that the Sharpe family had originally been from the upstate but had moved to the coastal region when the city had first been The Versailles Conspiracy
7.
Upon their move to the area, the Sharpe family had started a small business renting out rooms in their home to visitors
8.
The success story swells from there with the Sharpe family becoming one of the largest and most prominent developers in the area, owning everything from raw land to hotels to retail outlets and restaurants
9.
It was no wonder her father had not wanted Martha to marry into a family that could bring scandal and tarnish the Sharpe name
10.
A study by Sharpe Partners, an interactive marketing agency, revealed that 89% of
11.
In fact, the fixed fractional approach would have a lower Sharpe ratio for a commensurate return
12.
This is critically important: the asymmetrical risk profile compromises the relevance of simplistic measures such as the Sharpe ratio or the coefficient of variation
13.
coefficient of variation Obtained by dividing the standard deviation by the mean—conceptually this is similar to the reciprocal of the Sharpe ratio with the risk-free rate set to zero
14.
Sharpe, a Nobel laureate and a typical efficient market believer, stated in his book Investments: that if you can assume an efficient market, “every security price equals its investment value at all times
15.
Sharpe, a Nobel laureate and a typical efficient-market believer, stated in the third edition of his book Investments that if you assume an efficient market, “every security’s price equals its investment value at all times”
16.
1 documents raw annualized compound average returns (nominal geometric means) and risk-adjusted returns (Sharpe ratios), as well as some risk statistics, for various investments over the period 1990–2009
17.
The Sharpe ratio (henceforth SR) is the annualized arithmetic mean excess return over cash, divided by its annualized volatility; cash can be represented by the deposit rate (here) or by the Treasury bill rate (Chapter 3)
18.
I will later return to one key exception, which is that buying short-dated (1-to-3-year) top-rated (AAA/AA) credits while shorting duration-matched Treasuries earned a high Sharpe ratio
19.
Both positive illiquidity premia and the understatement of risk in the denominator of the Sharpe ratio calculation imply that we should observe higher Sharpe ratios for less liquid assets
20.
8% and the Sharpe ratio 0
21.
The Sharpe ratio is closely related to statistical significance
22.
The denominator of a Sharpe ratio only includes σ
23.
) Given a 20-year sample period, an asset’s annual excess return is statistically significantly above zero if the Sharpe ratio exceeds 0
24.
[4] Expressing the same contrast in Sharpe ratio terms, global bonds beat stocks hands down, 0
25.
Despite unexpected windfall gains, longest duration bonds have clearly lower Sharpe ratios than short-dated bonds, because of the higher volatility of long-dated issues
26.
In contrast to what I do in Chapter 2, the excess returns and Sharpe ratios here use the return on one-month Treasury bills, rather than somewhat higher deposit rates, as the riskless rate
27.
Some of the long-run Sharpe ratios are based on annual data
28.
Specifically, the Sharpe ratio (SR) is the average excess return over the riskless rate of return (proxied, in practice, by a near-riskless money market asset) divided by the volatility of this excess return
29.
[3] Sharpe ratio and relative return investors: The information ratio is the benchmark-oriented relative return manager’s counterpart to an absolute return manager’s Sharpe ratio
30.
Sharpe ratio is sometimes computed as the ratio of total return and its volatility, which is plain wrong; the return on a money market asset should be subtracted from total returns
31.
The capital asset pricing model (CAPM), originated by Sharpe, Lintner, Mossin, and Treynor, was the profession’s first answer and, for a long time, the principal one [1]
32.
• I show empirically that many strategies with the best Sharpe ratios since the 1980s are of the second type
33.
This feature can largely explain their high Sharpe ratios
34.
It is harder to explain the performance of government bonds since the 1980s as an equilibrium outcome, given the combination of a high Sharpe ratio and a wonderful diversification/hedging role
35.
As noted, the high in-sample Sharpe ratios of Treasuries over that time frame likely reflect windfall gains from unanticipated yield declines
36.
Note that the Sharpe ratios of Treasuries over periods ending in the early 1980s were very poor, reflecting windfall losses from unanticipated yield increases—a mirror image of the situation from the early 1980s to the present
37.
Moreover, when investors expect improving macroeconomic conditions they tend to expect higher equity returns and lower volatility; this result provides direct evidence of procyclical expected Sharpe ratios
38.
Amromin and Sharpe (2009) argue that these results lend support to behavioral explanations related to representativeness: optimism regarding the macroeconomy translates (too) directly into optimism on stock market prospects
39.
Many studies document countercyclical ex ante Sharpe ratios based on valuation ratios or yield curve steepness and then assume that such predictability reflects investors’ rational risk assessments and preferences
40.
At least retail investors’ subjective return expectations exhibit procyclical expected Sharpe ratios in a manner consistent with behavioral sentiment stories
41.
Indeed, the Sharpe ratios at short maturities exceed one (if the one-month Treasury bill is used as the riskless rate) and decline monotonically from the shortest to the longest portfolios
42.
Average Sharpe ratios are especially high at short maturities, and the reward–risk curve is very steep at the front end (with longer maturities providing higher returns) even in the bond-bearish subsample
43.
Ex ante Sharpe ratios (e
44.
, spread per unit of volatility) have persistently been higher for top-rated front-end carry trades than for most other credit trades—and ex post Sharpe ratios have broadly reflected delivery of these promised outcomes
45.
Mechanically, high ex ante Sharpe ratios reflect large spread–duration ratios (i
46.
Together these features explain high ex ante Sharpe ratios—and lesser ex post Sharpe ratios
47.
Why has this opportunity—with persistently high ex ante Sharpe ratios—not been arbitraged away?
48.
Incorporating funding rate spreads cuts the information or Sharpe ratio of the aggregate trade from 0
49.
When leverage is restricted, less capital gets devoted to front-end trades that lack inherent volatility (and thus require leverage to achieve meaningful returns), so that arbitrage opportunities are less fully exploited and Sharpe ratios are higher
50.
In the mid-2000s, ex ante Sharpe ratios declined both because Treasury holders gradually became more conscious of the opportunity cost of their low-returning holdings and because more levered capital became available to pursue any remaining “arbitrage” opportunities
51.
Emerging markets debt has one of the best long-run returns and Sharpe ratios of any asset class in the 1990s and 2000s
52.
Smoothing understates measured volatility and overstates Sharpe ratios, and any risk measures that rely on correlations are further understated
53.
Although the MIT-CRE index and the NCREIF index have comparable long-run returns, the former has volatility that is twice as high since it is not as artificially smoothed, so its measured Sharpe ratio is lower—but more realistic [4]
54.
All approaches appear to boost returns and Sharpe ratios but they also involve higher trading costs (and, likely, fees)
55.
3% and a Sharpe ratio of 1
56.
Even the more realistic representation in the HFR FoF index achieved a Sharpe ratio of 0
57.
The high Sharpe ratios discussed earlier partly reflect various reporting biases (survivor, backfill, etc
58.
Second, many HFs load on various risks that the Sharpe ratio does not capture well
59.
Most styles earned double-digit returns and all styles except short-selling equities achieved a high Sharpe ratio
60.
Short-sellers are the exception—this group’s low Sharpe ratio is consistent with its superior diversification ability
61.
That is, we should expect lower returns and lower Sharpe ratios than in the past, merely due to competitive pressures
62.
Yet others stress that institutional investors required lower volatility and accepted lower Sharpe ratios than traditional HF investors, making single-digit returns and volatilities the new norm
63.
The statement, “Too much money chasing the finite dollar supply of alpha will reduce HF Sharpe ratios”, initially sounds plausible but upon reflection is problematic:• There have been some attempts to estimate this finite alpha supply; one might, for example, suppose that smart alpha hunters can extract some fraction, say 50 bp, of the aggregate capitalization of the global capital market each year, or directly from underperforming long-only managers and retail investors, before hunters’ activity triggers a regulatory backlash
64.
• Moreover, the gross alpha pool among all investors is zero, by definition (“the arithmetic of active management” according to Sharpe, 1991)
65.
value premium has been similarly impressive since 1975 and its long-run Sharpe ratio is even higher due to better diversification across many countries and the use of four different valuation ratios to construct it
66.
the rolling 60-month Sharpe ratio has been positive through most of available history, with the main exceptions being in 1932 and 1999
67.
The consistency of the results is impressive: all strategies have positive Sharpe ratios, ranging between 0
68.
The complementary nature (negative correlation) of value and momentum strategies means that combining the two can sharply reduce portfolio volatility and boost Sharpe ratios:• One of my favourite clichés is “when value and momentum clash, value almost always loses first
69.
• Carry strategies within G10 markets have an attractive long-run Sharpe ratio—which is even higher in emerging markets and higher if refinements or carry timing are used
70.
Despite recent losses, long-run Sharpe ratios for currency carry strategies are higher than for equities, fixed income, or credit
71.
5% volatility, and a Sharpe ratio (SR) of 0
72.
The more popular and successful variant of carry trading involves dividing carry by some volatility measure, effectively giving us an ex ante Sharpe ratio as the trading signal
73.
Scaling position sizes inversely by recent historical or option-implied volatility tends to improve Sharpe ratios
74.
4%, with 12% volatility, and a Sharpe ratio of 1
75.
Incorporating these two seasonal biases would easily improve backtested FX carry strategy performance—for example, doubling position sizes for January and halving sizes for the rest of the year if the January return had been negative would have boosted the Sharpe ratio since 1983 from 0
76.
Persistent success in turn attracts return-chasing inflows, which improves Sharpe ratios further and results in overvaluation and overcrowding
77.
As it gradually emerged that carry return distribution is asymmetric, academics began to explore whether this negative skew could explain high average returns and Sharpe ratios as a risk premium
78.
The long-run realized Sharpe ratio above 1 for carry strategies, widely reported in the mid-2000s, was never sustainable, as it included a period of overvaluation and overcrowding but not its unwind
79.
) The lower long-term Sharpe ratios for periods that include the implosion are more representative of “the full cycle” and are more unbiased guides for the future
80.
The Sharpe ratio of the 2000s’ decade would have been halved—but the losses would have already been offset within two years and long-term strategy performance still looks good with hindsight:• To prevent hyperinflation-related currency losses, the first defense is smart country selection—ruling out from the trading universe any countries that might plausibly drift into hyperinflation
81.
I have documented abnormally high Sharpe ratios for trend following in bonds in the week ahead of payroll reports (see Ilmanen–Byrne, 2003)
82.
Contrasting Sharpe ratios for trading strategies that buy past winners and sell recent losers based on recent and intermediate momentum (in four equity market contexts and in two others)
83.
Less scrupulous managers may also prefer a high probability of positive returns so that they can accumulate large fees before a rare disaster materializes, especially since overstated smoothness of returns can boost the Sharpe ratio and attract larger AUM until the blowup occurs
84.
Specifically, Broadie–Chernov–Johannes (2009) argue that options are often thought to be mispriced because the performance metrics that are used (Sharpe ratios and CAPM alphas) are ill-suited for option analysis, especially over short samples
85.
More tactically, stock markets in countries with especially high or low GDP growth rates over the preceding 5 years subsequently earned similar Sharpe ratios as markets in countries with middling past growth
86.
2 shows a similar scatterplot but Sharpe ratio on the y-axis
87.
Since volatility is an insufficient risk measure, reasonable investors may accept a lower portfolio Sharpe ratio if they can trade it off against better diversification characteristics, more attractive asymmetry, higher liquidity, and lesser tail risks
88.
Even if expected returns were unchanged, such a rise would imply lower ex ante Sharpe ratios and thus discourage investment
89.
These lotto investors are willing to sacrifice Sharpe ratio (mean variance efficiency) to get higher skewness
90.
This figure shows annualized Sharpe ratios of BAB factors across asset classes
91.
The BAB factor is a zero-cost portfolio that is long the low-beta portfolio and short the high-beta portfolio (Sharpe ratios are annualized)
92.
The model predicts high Sharpe ratios for portfolios that are long low-beta and short high-beta assets, scaled to similar beta levels
93.
Perold and Sharpe stressed that when contrarian strategies succeed for a while, they attract followers and markets may become too stable (too slow to adjust to economic developments)
94.
2 shows a stylized lifecycle of the ex ante Sharpe ratio
95.
If the regularity that caused the strategy to be profitable in the first place reflects a (time-varying) risk premium, the new equilibrium should involve a sustainably positive Sharpe ratio, albeit lower than before the regularity was widely known
96.
If the regularity reflects market inefficiency, the Sharpe ratio should converge toward zero once markets have learned about it
97.
To evaluate the model’s past track record, we can study the correlation of these fitted values with actual monthly excess returns; alternatively, we can compute the hit rate (how often the model predicted the correct sign of next month market direction) or, most practically, the Sharpe ratio of a trading rule based on the model’s prescribed positions
98.
High-turnover strategies (fast signals) implemented at high frequencies require either very high gross Sharpe ratios or low trading costs, preferably both
99.
Low-turnover strategies (slow signals) can afford lower gross Sharpe ratios or higher trading costs
100.
• After an overview, this chapter drills into each path and also contains essays on related topics such as rebalancing and diversification return, looking beyond the Sharpe ratio, and time diversification
