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Born June 16, 1934 (age 80)Boston, Massachusetts, U.S.

Nationality United States

Fields Economics

Institutions

William F. Sharpe AssociatesStanford UniversityUC IrvineUniversity of Washington 1961–68RAND Corporation

Known for Capital asset pricing modelSharpe ratio

Notable awards Nobel Memorial Prize in Economic Sciences (1990

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William Forsyth Sharpe

William Forsyth Sharpe (born June 16, 1934) is an American economist. He is the STANCO 25 Professor of Finance, Emeritus at Stanford University's Graduate School of Business, and the winner of the 1990 Nobel Memorial Prize in Economic Sciences.

Sharpe was one of the originators of the capital asset pricing model, created the Sharpe ratio for risk-adjusted investment performance analysis, contributed to the development of the binomial method for the valuation of options, the gradient method for asset allocation optimization, and returns-based style analysis for evaluating the style and performance of investment funds.

Sharpe ratio

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk (and is a deviation risk measure), named after William F. Sharpe.

Definition

Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as:

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where is the asset return, is the return on a benchmark asset, such as the risk free rate of return or an index such as the S&P 500. is the expected value of the excess of the asset return over the benchmark return, and is the standard deviation of this excess return. This is often confused with the information ratio, in part because the newer definition of the Sharpe ratio matches the definition of information ratio within the field of finance. Outside of this field, information ratio is simply mean over the standard deviation of a series of measurements.

The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns - see the second example below.

Use in finance

The Sharpe ratio characterizes how well the return of an asset compensates the investor for the risk taken. When comparing two assets versus a common benchmark, the one with a higher Sharpe ratio provides better return for the same risk (or, equivalently, the same return for lower risk). However, like any other mathematical model, it relies on the data being correct. Pyramid schemes with a long duration of operation would typically provide a high Sharpe ratio when derived from reported returns, but the inputs are false. When examining the investment performance of assets with smoothing of returns (such as with-profits funds) the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns.

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

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Tests

Several statistical tests of the Sharpe ratio have been proposed. These include those proposed by Jobson &Korkie and Gibbons, Ross &Shanken.

History

In 1952, Arthur D. Roy suggested maximizing the ratio "(m-d)/σ", where m is expected gross return, d is some "disaster level" (a.k.a., minimum acceptable return) and σ is standard deviation of returns. This ratio is just the Sharpe ratio, only using minimum acceptable return instead of the risk-free rate in the numerator, and using standard deviation of returns instead of standard deviation of excess returns in the denominator.

In 1966, William F. Sharpe developed what is now known as the Sharpe ratio.[1] Sharpe originally called it the "reward-to-variability" ratio before it began being called the Sharpe ratio by later academics and financial operators. The definition was:

Sharpe's 1994 revision acknowledged that the basis of comparison should be an applicable benchmark, which changes with time. After this revision, the definition is:

Note, if Rf is a constant risk-free return throughout the period,

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Recently, the (original) Sharpe ratio has often been challenged with regard to its appropriateness as a fund performance measure during evaluation periods of declining markets.

Examples

Suppose the asset has an expected return of 15% in excess of the risk free rate. We typically do not know if the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%. The risk-free return is constant. Then the Sharpe ratio (using the old definition) will be 1.5 ( and ).

For an example of calculating the more commonly used ex-post Sharpe ratio - which uses realized rather than expected returns - based on the contemporary definition, consider the following table of weekly returns.

Date Asset Return S&P 500 total return Excess Return

7/6/2012 -0.0050000 -0.0048419 -0.0001581

7/13/2012 0.0010000 0.0017234 -0.0007234

7/20/2012 0.0050000 0.0046110 0.0003890

We assume that the asset is something like a large-cap U.S. equity fund which would logically be benchmarked against the S&P 500. The mean of the excess returns is -0.0001642 and the (population) standard deviation is 0.0005562248, so the Sharpe ratio is -0.0001642/0.0005562248, or -0.2951444.

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Strengths and weaknesses

The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Other ratios such as the bias ratio have recently been introduced into the literature to handle cases where the observed volatility may be an especially poor proxy for the risk inherent in a time-series of observed returns.

While the Treynor ratio works only with systematic risk of a portfolio, the Sharpe ratio observes both systematic and idiosyncratic risks.

The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - not all asset returns are normally distributed. Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed.

Bailey and López de Prado (2012) show that Sharpe ratios tend to be overstated in the case of hedge funds with short track records. These authors propose a probabilistic version of the Sharpe ratio that takes into account the asymmetry and fat-tails of the returns' distribution. With regards to the selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a Sharpe ratio indifference curveThis curve illustrates the fact that it is efficient to hire portfolio managers with low and even negative Sharpe ratios, as long as their correlation to the other portfolio managers is sufficiently low.

Because it is a dimensionless ratio, laypeople find it difficult to interpret Sharpe ratios of different investments. For example, how much better is an investment with a Sharpe ratio of 0.5 than one with a Sharpe ratio of -

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0.2? This weakness was well addressed by the development of the Modigliani risk-adjusted performance measure, which is in units of percent return – universally understandable by virtually all investors. In some settings, the Kelly criterion can be used to convert the Sharpe ratio into a rate of return. (The Kelly criterion gives the ideal size of the investment, which when adjusted by the period and expected rate of return per unit, gives a rate of return.)

The accuracy of Sharpe ratio estimators hinges on the statistical properties of returns, and these properties can vary considerably among strategies, portfolios, and over tim

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Milton Friedman (July 31, 1912 – November 16, 2006) was an American economist, statistician and writer who taught at the University of Chicago for more than three decades. He received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the complexity of stabilization policy.

BornJuly 31, 1912Brooklyn, New York, USA

DiedNovember 16, 2006 (aged 94)San Francisco, California, USA

Nationality American

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Institution

Hoover Institution (1977–2006)Columbia University (1964–65)University of Chicago (1946–77)Columbia University (1937–41; 1943–45)National Bureau of Economic Research (1937–40)

School or tradition Chicago School

Alma materColumbia University (PhD 1946)University of Chicago (MA 1933)Rutgers University (BA 1932)

Contributions

Price theory · MonetarismApplied macroeconomicsFloating exchange ratesPermanent income hypothesisVolunteer military · Friedman test

AwardsNational Medal of Science (1988)Presidential Medal of Freedom (1988)Nobel Memorial Prize in Economic Sciences (1976)John Bates Clark Medal (1951)

Nobel Prize in Economic Sciences

Friedman won the Nobel Memorial Prize in Economic Sciences, the sole recipient for 1976, "for his achievements in the fields of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy."

In monetary economics, monetarism is a school of thought that emphasises the role of governments in controlling the amount of money in circulation. Monetarists believe that variation in the money supply has

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major influences on national output in the short run and the price level over longer periods, and that objectives of monetary policy are best met by targeting the growth rate of the money supply rather than by engaging in discretionary monetary policy.[1]

Monetarism today is mainly associated with the work of Milton Friedman, who was among the generation of economists to accept Keynesian economics and then criticise Keynes' theory of gluts using fiscal policy (government spending). Friedman and Anna Schwartz wrote an influential book, A Monetary History of the United States, 1867–1960, and argued "inflation is always and everywhere a monetary phenomenon." Though he opposed the existence of the Federal Reserve,[2] Friedman advocated, given its existence, a central bank policy aimed at keeping the supply and demand for money at equilibrium, as measured by growth in productivity and demand

India

Components of the money supply of India in billions of Rupee for 1950–2011

The Reserve Bank of India defines the monetary aggregates as:

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Reserve Money (M0): Currency in circulation + Bankers’ deposits with the RBI + ‘Other’ deposits with the RBI = Net RBI credit to the Government + RBI credit to the commercial sector + RBI’s claims on banks + RBI’s net foreign assets + Government’s currency liabilities to the public – RBI’s net non-monetary liabilities.

M1: Currency with the public + Deposit money of the public (Demand deposits with the banking system + ‘Other’ deposits with the RBI).

M2: M1 + Savings deposits with Post office savings banks. M3: M1+ Time deposits with the banking system = Net bank credit to the

Government + Bank credit to the commercial sector + Net foreign exchange assets of the banking sector + Government’s currency liabilities to the public – Net non-monetary liabilities of the banking sector (Other than Time Deposits).

M4: M3 + All deposits with post office savings banks (excluding National Savings Certificates).

Link with inflation

Monetary exchange equation

Money supply is important because it is linked to inflation by the equation of exchange in an equation proposed by Irving Fisher in 1911:

where

is the total dollars in the nation’s money supply, is the number of times per year each dollar is spent (velocity of money), is the average price of all the goods and services sold during the year, is the quantity of assets, goods and services sold during the year.

In mathematical terms, this equation is really an identity which is true by definition rather than describing economic behavior. That is, each term is

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defined by the values of the other three. Unlike the other terms, the velocity of money has no independent measure and can only be estimated by dividing PQ by M. Some adherents of the quantity theory of money assume that the velocity of money is stable and predictable, being determined mostly by financial institutions. If that assumption is valid then changes in M can be used to predict changes in PQ. If not, then a model of V is required in order for the equation of exchange to be useful as a macroeconomics model or as a predictor of prices.

Most macroeconomists replace the equation of exchange with equations for the demand for money which describe more regular and predictable economic behavior. However, predictability (or the lack thereof) of the velocity of money is equivalent to predictability (or the lack thereof) of the demand for money (since in equilibrium real money demand is simply Q/V). Either way, this unpredictability made policy-makers at the Federal Reserve rely less on the money supply in steering the U.S.economy. Instead, the policy focus has shifted to interest rates such as the fed funds rate.

In practice, macroeconomists almost always use real GDP to measure Q, omitting the role of all transactions except for those involving newly produced goods and services (i.e., consumption goods, investment goods, government-purchased goods, and exports). That is, the only assets counted as part of Q are newly produced investment goods. But the original quantity theory of money did not follow this practice: PQ was the monetary value of all new transactions, whether of real goods and services or of paper assets.

U.S. M3 money supply as a proportion of gross domestic product.

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The monetary value of assets, goods, and service sold during the year could be grossly estimated using nominal GDP back in the 1960s. This is not the case anymore because of the dramatic rise of the number of financial transactions relative to that of real transactions up until 2008. That is, the total value of transactions (including purchases of paper assets) rose relative to nominal GDP (which excludes those purchases).

Ignoring the effects of monetary growth on real purchases and velocity, this suggests that the growth of the money supply may cause different kinds of inflation at different times. For example, rises in the U.S. money supplies between the 1970s and the present encouraged first a rise in the inflation rate for newly produced goods and services ("inflation" as usually defined) in the seventies and then asset-price inflation in later decades: it may have encouraged a stock market boom in the '80s and '90s and then, after 2001, a rise in home prices, i.e., the famous housing bubble. This story, of course, assumes that the amounts of money were the causes of these different types of inflation rather than being endogenous results of the economy's dynamics.

When home prices went down, the Federal Reserve kept its loose monetary policy and lowered interest rates; the attempt to slow price declines in one asset class, e.g. real estate, may well have caused prices in other asset classes to rise, e.g. commodities

Rates of growth

In terms of percentage changes (to a close approximation under small growth rates, the percentage change in a product, say XY, is equal to the sum of the percentage changes %ΔX + %ΔY). So:

%ΔP + %ΔQ = %ΔM + %ΔV

That equation rearranged gives the "basic inflation identity":

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%ΔP = %ΔM + %ΔV – %ΔQ

Inflation (%ΔP) is equal to the rate of money growth (%ΔM), plus the change in velocity (%ΔV), minus the rate of output growth (%ΔQ). As before, this equation is only useful if %ΔV follows regular behavior. It also loses usefulness if the central bank lacks control over %ΔM.

Bank reserves at central bank

When a central bank is "easing", it triggers an increase in money supply by purchasing government securities on the open market thus increasing available funds for private banks to loan through fractional-reserve banking (the issue of new money through loans) and thus the amount of bank reserves and the monetary base rise. By purchasing government bonds (e.g., U.S. Treasury bills), this bids up their prices, so that interest rates fall at the same time that the monetary base increases.

With "easy money," the central bank creates new bank reserves (in the US known as "federal funds"), which allow the banks lend more. These loans get spent, and the proceeds get deposited at other banks. Whatever is not required to be held as reserves is then lent out again, and through the "multiplying" effect of the fractional-reserve system, loans and bank deposits go up by many times the initial injection of reserves.

In contrast, when the central bank is "tightening", it slows the process of private bank issue by selling securities on the open market and pulling money (that could be loaned) out of the private banking sector. By increasing the supply of bonds, this lowers their prices and raises interest rates at the same time that the money supply is reduced.

This kind of policy reduces or increases the supply of short term government debt in the hands of banks and the non-bank public, lowering or raising interest rates. In parallel, it increases or reduces the supply of

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loanable funds (money) and thereby the ability of private banks to issue new money through issuing debt.

The simple connection between monetary policy and monetary aggregates such as M1 and M2 changed in the 1970s as the reserve requirements on deposits started to fall with the emergence of money funds, which require no reserves. Then in the early 1990s, reserve requirements, for example in Canada, were dropped to zeroon savings deposits, CDs, and Eurodollar deposit. At present, reserve requirements apply only to "transactions deposits" – essentially checking accounts. The vast majority of funding sources used by private banks to create loans are not limited by bank reserves. Most commercial and industrial loans are financed by issuing large denomination CDs. Money market deposits are largely used to lend to corporations who issue commercial paper. Consumer loans are also made using savings deposits, which are not subject to reserve requirements. This means that instead of the amount of loans supplied responding passively to monetary policy, we often see it rising and falling with the demand for funds and the willingness of banks to lend.

Some academics argue that the money multiplier is a meaningless concept, because its relevance would require that the money supply be exogenous, i.e. determined by the monetary authorities via open market operations. If central banks usually target the shortest-term interest rate (as their policy instrument) then this leads to the money supply being endogenous.[45]

Neither commercial nor consumer loans are any longer limited by bank reserves. Nor are they directly linked proportional to reserves. Between 1995 and 2008, the amount of consumer loans has steadily increased out of proportion to bank reserves. Then, as part of the financial crisis, bank reserves rose dramatically as new loans shrank.

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In recent years, some academic economists renowned for their work on the implications of rational expectations have argued that open market operations are irrelevant. These include Robert Lucas, Jr., Thomas Sargent, Neil Wallace, Finn E. Kydland, Edward C. Prescott and Scott Freeman. The Keynesian side points to a major example of ineffectiveness of open market operations encountered in 2008 in the United States, when short-term interest rates went as low as they could go in nominal terms, so that no more monetary stimulus could occur. This zero bound problem has been called the liquidity trap or "pushing on a string" (the pusher being the central bank and the string being the real economy).

Arguments

The main functions of the central bank are to maintain low inflation and a low level of unemployment, although these goals are sometimes in conflict (according to Phillips curve). A central bank may attempt to do this by artificially influencing the demand for goods by increasing or decreasing the nation's money supply (relative to trend), which lowers or raises interest rates, which stimulates or restrains spending on goods and services.

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An important debate among economists in the second half of the twentieth century concerned the central bank's ability to predict how much money should be in circulation, given current employment rates and inflation rates. Economists such as Milton Friedman believed that the central bank would always get it wrong, leading to wider swings in the economy than if it were just left alone.[46] This is why they advocated a non-interventionist approach—one of targeting a pre-specified path for the money supply independent of current economic conditions— even though in practice this might involve regular intervention with open market operations (or other monetary-policy tools) to keep the money supply on target.

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