alpha beta gamma finance

8/17/2019 Alpha Beta Gamma Finance

1/15

Alpha (finance)Alpha is a measure of the so-called active return on an investment, the performance of thatinvestment compared to a suitable market index. An alpha of 1 means the investment's return oninvestment over a selected period of time was 1% better than the market during that same

period, an alpha of -1 means the investment underperformed the market. Alpha is one of the fivekey measures in modern portfolio theory.

n modern financial markets, where index funds are widely available for purchase, alpha iscommonly used to !udge the performance of mutual funds and similar investments. As thesefunds include various fees normally expressed in percent terms, the fund has to maintain analpha greater than its fees in order to provide positive gains compared to an index fund."istorically, the vast ma!ority of traditional funds have had negative alphas, which has led toa flight of capital to index funds and non-traditional hedge funds.

t is also possible to analy#e a portfolio of investments and calculate a theoretical performance,most commonly using thecapital asset pricing model $A&(. )eturns on that portfolio can becompared to the theoretical returns, in which case the measure is known as *ensen's alpha. +hisis useful for non-traditional or highly focused funds, where a single stock index might not berepresentative of the investment's holdings.

Definitionedit

+he alpha coefficient $ ( is a parameter in the capital asset pricing model $A&(. t isthe intercept of the security characteristic line $/(, that is, the coefficient of the constant in amarket model regression.

t can be shown that in an efficient market, the expected value of the alpha coefficient is#ero. +herefore the alpha coefficient indicates how an investment has performed after

accounting for the risk it involved0

• 0 the investment has earned too little for its risk $or, was too risky for the return(

• 0 the investment has earned a return adeuate for the risk taken

• 0 the investment has a return in excess of the reward for the assumed risk

2or instance, although a return of 34% may appear good, the investment can still have anegative alpha if it's involved in an excessively risky position.

Origin of the concept A belief in efficient markets spawned the creation of market capitali#ation weighted indexfunds that seek to replicate the performance of investing in an entire market in the weightsthat each of the euity securities comprises in the overall market. citation needed +he best examplesfor the 5 are the 6& 744 and the 8ilshire 7444 which approximately represent the 744most widely held euities and the largest 7444 securities respectively, accounting forapproximately 94%: and ;;%: of the total market capitali#ation of the 5 market as awhole.

n fact, to many investors,citation needed this phenomenon created a new standard of performancethat must be matched0 an investment manager should not only avoid losing money for theclient and should make a certain amount of money, but in fact should make more moneythan the passive strategy of investing in everything eually $since this strategy appeared tobe statistically more likely to be successful than the strategy of any one investment

https://en.wikipedia.org/wiki/Active_returnhttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Stock_market_indexhttps://en.wikipedia.org/wiki/Return_on_investmenthttps://en.wikipedia.org/wiki/Return_on_investmenthttps://en.wikipedia.org/wiki/Modern_portfolio_theoryhttps://en.wikipedia.org/wiki/Modern_portfolio_theoryhttps://en.wikipedia.org/wiki/Index_fundhttps://en.wikipedia.org/wiki/Index_fundhttps://en.wikipedia.org/wiki/Mutual_fundhttps://en.wikipedia.org/wiki/Flight_of_capitalhttps://en.wikipedia.org/wiki/Hedge_fundhttps://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Jensen's_alphahttps://en.wikipedia.org/w/index.php?title=Alpha_(finance)&action=edit&section=1https://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Root_of_a_functionhttps://en.wikipedia.org/wiki/Root_of_a_functionhttps://en.wikipedia.org/wiki/Security_characteristic_linehttps://en.wikipedia.org/wiki/Efficient-market_hypothesishttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/S%26P_500https://en.wikipedia.org/wiki/S%26P_500https://en.wikipedia.org/wiki/Wilshire_5000https://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Stock_market_indexhttps://en.wikipedia.org/wiki/Return_on_investmenthttps://en.wikipedia.org/wiki/Return_on_investmenthttps://en.wikipedia.org/wiki/Modern_portfolio_theoryhttps://en.wikipedia.org/wiki/Index_fundhttps://en.wikipedia.org/wiki/Mutual_fundhttps://en.wikipedia.org/wiki/Flight_of_capitalhttps://en.wikipedia.org/wiki/Hedge_fundhttps://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Jensen's_alphahttps://en.wikipedia.org/w/index.php?title=Alpha_(finance)&action=edit&section=1https://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Root_of_a_functionhttps://en.wikipedia.org/wiki/Security_characteristic_linehttps://en.wikipedia.org/wiki/Efficient-market_hypothesishttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/S%26P_500https://en.wikipedia.org/wiki/Wilshire_5000https://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Active_return


2/15

manager(. +he name for the additional return above the expected return of the beta ad!ustedreturn of the market is called


3/15

Beta (finance)n finance, the beta $?( of an investment is a measure of the risk arising from exposure to

general market movements as opposed to idiosyncratic factors. +he market portfolio of all

investable assets has a beta of exactly 1. A beta below 1 can indicate either an investment with

lower volatility than the market, or a volatile investment whose price movements are not

highly correlated with the market. An example of the first is a treasury bill0 the price does not go

up or down a lot, so it has a low beta. An example of the second is gold. +he price of gold does

go up and down a lot, but not in the same direction or at the same time as the market. 1

A beta greater than one generally means that the asset both is volatile and tends to move up and

down with the market. An example is a stock in a big technology company. @egative betas are

possible for investments that tend to go down when the market goes up, and vice versa. +here

are few fundamental investments with consistent and significant negative betas, but

some derivatives like euity put options can have large negative betas.3

=eta is important because it measures the risk of an investment that cannot be reduced

by diversification. t does not measure the risk of an investment held on a stand-alone basis, but

the amount of risk the investment adds to an already-diversified portfolio. n the capital asset

pricing model, beta risk is the only kind of risk for which investors should receive an expected

return higher than the risk-free rate of interest.

+he definition above covers only theoretical beta. +he term is used in many related ways in

finance. 2or example, the betas commonly uoted in mutual fund analyses generally measure

the risk of the fund arising from exposure to a benchmark for the fund, rather than from exposure

to the entire market portfolio. +hus they measure the amount of risk the fund adds to a diversified

portfolio of funds of the same type, rather than to a portfolio diversified among all fund types. B

=eta decay refers to the tendency for a company with a high beta coefficient $? C 1( to have its

beta coefficient decline to the market beta. t is an example of regression toward the mean.

Statistical estimationedit

=eta is estimated by regression. Diven an asset and a benchmark that we are interested in, we

want to find an approximate formula

where r a is the return of the asset and r b is return of the benchmark.

ince the data are usually in the form of time series, the statistical model is

,

https://en.wikipedia.org/wiki/Financehttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Market_(economics)https://en.wikipedia.org/wiki/Market_portfoliohttps://en.wikipedia.org/wiki/Market_portfoliohttps://en.wikipedia.org/wiki/Assethttps://en.wikipedia.org/wiki/Volatility_(finance)https://en.wikipedia.org/wiki/Volatility_(finance)https://en.wikipedia.org/wiki/Correlation_and_dependencehttps://en.wikipedia.org/wiki/Correlation_and_dependencehttps://en.wikipedia.org/wiki/United_States_Treasury_securityhttps://en.wikipedia.org/wiki/Goldhttps://en.wikipedia.org/wiki/Goldhttps://en.wikipedia.org/wiki/Goldhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-1https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Equity_(finance)https://en.wikipedia.org/wiki/Equity_(finance)https://en.wikipedia.org/wiki/Equity_(finance)https://en.wikipedia.org/wiki/Put_optionhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-2https://en.wikipedia.org/wiki/Diversification_(finance)https://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Risk-free_interest_ratehttps://en.wikipedia.org/wiki/Risk-free_interest_ratehttps://en.wikipedia.org/wiki/Risk-free_interest_ratehttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-3https://en.wikipedia.org/wiki/Mutual_fundhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-4https://en.wikipedia.org/wiki/Regression_toward_the_meanhttps://en.wikipedia.org/wiki/Regression_toward_the_meanhttps://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=1https://en.wikipedia.org/wiki/Time_serieshttps://en.wikipedia.org/wiki/Financehttps://en.wikipedia.org/wiki/Investmenthttps://en.wikipedia.org/wiki/Market_(economics)https://en.wikipedia.org/wiki/Market_portfoliohttps://en.wikipedia.org/wiki/Assethttps://en.wikipedia.org/wiki/Volatility_(finance)https://en.wikipedia.org/wiki/Correlation_and_dependencehttps://en.wikipedia.org/wiki/United_States_Treasury_securityhttps://en.wikipedia.org/wiki/Goldhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-1https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Equity_(finance)https://en.wikipedia.org/wiki/Put_optionhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-2https://en.wikipedia.org/wiki/Diversification_(finance)https://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Capital_asset_pricing_modelhttps://en.wikipedia.org/wiki/Risk-free_interest_ratehttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-3https://en.wikipedia.org/wiki/Mutual_fundhttps://en.wikipedia.org/wiki/Beta_(finance)#cite_note-4https://en.wikipedia.org/wiki/Regression_toward_the_meanhttps://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=1https://en.wikipedia.org/wiki/Time_series


4/15

where Et is an error term $the unexplained return(. lick here for a definition of Alpha $F(.

+he best $in the sense of least suared error( estimates for F and ? are those such that GE t 3 is as

small as possible.

A common expression for beta is

,

where ov and Har are the covariance and variance operators.

+his can also be expressed as

where Ia,b is the correlation of the two returns, and Ja and Jb are the respective volatilities.

)elationships between standard deviation, variance and

correlation0

=eta can be computed for prices in the past, where the data is known, which is historical beta.

"owever, what most people are interested in is future beta, which relates to risks going forward.

Kstimating future beta is a difficult problem. Lne guess is that future beta euals historical beta.

2rom this, we find that beta can be explained as


5/15

is called the asset's alpha and is called the asset's beta coefficient. =oth coefficients

have an important role inmodern portfolio theory.

2or example, in a year where the broad market or benchmark index returns 37% above the risk

free rate, suppose two managers gain 74% above the risk free rate. =ecause this higher return is

theoretically possible merely by taking aleveraged position in the broad market to double the

beta so it is exactly 3.4, we would expect a skilled portfolio manager to have built the

outperforming portfolio with a beta somewhat less than 3, such that the excess return not

explained by the beta is positive. f one of the managers' portfolios has an average beta of .4,

and the other's has a beta of only 1.7, then the A& simply states that the extra return of the

first manager is not sufficient to compensate us for that manager's risk, whereas the second

manager has done more than expected given the risk. 8hether investors can expect the second

manager to duplicate that performance in future periods is of course a different uestion.

Security market lineedit

The Security Market Line

+he / graphs the results from the capital asset pricing model $A&( formula. +he x -axis

represents the risk $beta(, and the y -axis represents the expected return. +he market risk

premium is determined from the slope of the /.

+he relationship between ? and reuired return is plotted on the security market line$/( whichshows expected return as a function of ?. +he intercept is the nominal risk-free rate available for

the market, while the slope is K$R m(M R f . +he security market line can be regarded as

representing a single-factor model of the asset price, where =eta is exposure to changes in value

of the arket. +he euation of the / is thus0

t is a useful tool in determining if an asset being considered for a portfolio offers a reasonable

expected return for risk. ndividual securities are plotted on the / graph. f the security's risk

versus expected return is plotted above the /, it is undervalued because the investor can

https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/wiki/Modern_portfolio_theoryhttps://en.wikipedia.org/wiki/Benchmark_(surveying)https://en.wikipedia.org/wiki/Leverage_(finance)https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=2https://en.wikipedia.org/wiki/Security_market_linehttps://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/wiki/Modern_portfolio_theoryhttps://en.wikipedia.org/wiki/Benchmark_(surveying)https://en.wikipedia.org/wiki/Leverage_(finance)https://en.wikipedia.org/wiki/Alpha_(finance)https://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=2https://en.wikipedia.org/wiki/Security_market_line


6/15

expect a greater return for the inherent risk. A security plotted below the / is overvalued

because the investor would be accepting a lower return for the amount of risk assumed.

Choice of benchmark edit

n the 5.., published betas typically use a stock market index such as the 6& 744 as a

benchmark. +he 6& 744 is a popular index of 5.. large-cap stocks. Lther choices may be an

international index such as the KA2K. +he benchmark is often chosen to be similar to the

assets chosen by the investor. 2or example, for a person who owns 6& 744 index funds and

gold bars, the index would combine the 6& 744 and the price of gold. n practice a standard

index is used.

+he choice of the index need not reflect the portfolio under uestionN e.g., beta for gold bars

compared to the 6& 744 may be low or negative carrying the information that gold does not

track stocks and may provide a mechanism for reducing risk. +he restriction to stocks as a

benchmark is somewhat arbitrary. A model portfolio may be stocks plus bonds. ometimes themarket is defined as


7/15

Adding to a portfolioedit

uppose an investor has all his money in an asset class Q and wishes to move a small amount

to an asset class R. 2or example, Q could be 5.. stocks, while R could be stocks of a different

country, or bonds. +hen the new portfolio, S, can be expressed symbolically

+he variance can be computed as

which can be simplified by ignoring T3 terms0

+he first formula is exact, while the second one is only valid for small T. 5sing the formula for ?

of R relative to Q,

we can compute

+his suggests that an asset with ? greater than one will increase variance, while an asset with ?

less than one will decrease variance, if added in the right amount. +his assumes that variance is

an accurate measure of risk, which is usually good. "owever, the beta does need to be

computed with respect to what the investor currently owns.

Academic theory edit

Academic theory claims that higher-risk investments should have higher returns over the long-

term. 8all treet has a saying that


8/15

where0

K K P firm's cost of euity

R 2 P risk-free rate $the rate of return on a


9/15

with a real example involving A+6+ nc. +he graph showing monthly returns from A+6+ is visibly

more volatile than the index and yet the standard estimate of beta for this is less than one.

+he relative volatility ratio described above is actually known as +otal =eta $at least by appraisers

who practice business valuation(. +otal beta is eual to the identity0 betaUR or the standard

deviation of the stockUstandard deviation of the market $note0 the relative volatility(. +otal betacaptures the security's risk as a stand-alone asset $because the correlation coefficient, ), has

been removed from beta(, rather than part of a well-diversified portfolio. =ecause appraisers

freuently value closely held companies as stand-alone assets, total beta is gaining acceptance

in the business valuation industry. Appraisers can now use total beta in the following euation0

total cost of euity $+LK( P risk-free rate : total betaVeuity risk premium. Lnce appraisers

have a number of +LK benchmarks, they can compareUcontrast the risk factors present in

these publicly traded benchmarks and the risks in their closely held company to better

defendUsupport their valuations.

Interpretations of Betaome interpretations of beta are explained in the following table0 ;

https://en.wikipedia.org/wiki/AT%26T_Inc.https://en.wikipedia.org/wiki/Beta_(finance)#cite_note-WikinvestBeta-9https://en.wikipedia.org/wiki/AT%26T_Inc.https://en.wikipedia.org/wiki/Beta_(finance)#cite_note-WikinvestBeta-9


10/15

t measures the part of the asset's statistical variance that cannot be removed by

the diversification provided by the portfolio of many risky assets, because of the correlation of its

returns with the returns of the other assets that are in the portfolio. =eta can be estimated forindividual companies using regression analysis against a stock market index. An alternative to

standard beta is downside beta.

=eta is always measured in respect to some benchmark. +herefore, an asset may have different

betas depending on which benchmark is used. *ust a number is useless if the benchmark is not

known.

"#treme and interesting cases

=eta has no upper or lower bound, and betas as large as or B will occur with highly volatilestocks.

Value

of

Beta

Interpretation Example

β < 0

Asset generally moves in the

opposite direction as compared

to the index

An inverse exchange-traded fund or a

short position

β 0

Movement of the asset is

uncorrelated !ith the movement

of the "enchmark

#ixed-yield asset$ !hose gro!th is

unrelated to the movement of the

stock market

0 < β

< %


generally in the same direction

as$ "ut less than the movement

of the "enchmark

Sta"le$ &staple& stock such as acompany that makes soap' Moves in

the same direction as the market at

large$ "ut less suscepti"le to day-to-

day (uctuation'

β %



as$ and a"out the same amount

as the movement of the

"enchmark

A representative stock$ or a stock that

is a strong contri"utor to the index

itself'

β ) %



as$ "ut more than the movement

of the "enchmark

Stocks !hich are very strongly

in(uenced "y day-to-day market ne!s$

or "y the general health of the

economy'

https://en.wikipedia.org/wiki/Variancehttps://en.wikipedia.org/wiki/Diversification_(finance)https://en.wikipedia.org/wiki/Diversification_(finance)https://en.wikipedia.org/wiki/Correlationhttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Stock_market_indexhttps://en.wikipedia.org/wiki/Stock_market_indexhttps://en.wikipedia.org/wiki/Downside_betahttps://en.wikipedia.org/wiki/Downside_betahttps://en.wikipedia.org/wiki/Inverse_exchange-traded_fundhttps://en.wikipedia.org/wiki/Variancehttps://en.wikipedia.org/wiki/Diversification_(finance)https://en.wikipedia.org/wiki/Correlationhttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Stock_market_indexhttps://en.wikipedia.org/wiki/Downside_betahttps://en.wikipedia.org/wiki/Inverse_exchange-traded_fund


11/15

=eta can be #ero. ome #ero-beta assets are risk-free, such as treasury bonds and cash. "owever, simply because a beta is #ero does not mean that it is risk-free. A beta can be #erosimply because the correlation between that item's returns and the market's returns is #ero. Anexample would be betting on horse racing. +he correlation with the market will be #ero, but it iscertainly not a risk-free endeavor.

Ln the other hand, if a stock has a moderately low but positive correlation with the market, but ahigh volatility, then its beta may still be high.

A negative beta simply means that the stock is inversely correlated with the market.

A negative beta might occur even when both the benchmark index and the stock underconsideration have positive returns. t is possible that lower positive returns of the index coincidewith higher positive returns of the stock, or vice versa. +he slope of the regression line in such acase will be negative.

5sing beta as a measure of relative risk has its own limitations. ost analyses consider only the

magnitude of beta. =eta is a statistical variable and should be considered with its statisticalsignificance $) suare value of the regression line(. "igher ) suare value implieshigher correlation and a stronger relationship between returns of the asset and benchmark index.

f beta is a result of regression of one stock against the market where it is uoted, betas fromdifferent countries are not comparable.

5tility stocks commonly show up as examples of low beta. +hese have some similarity to bonds,in that they tend to pay consistent dividends, and their prospects are not strongly dependent oneconomic cycles. +hey are still stocks, so the market price will be affected by overall stockmarket trends, even if this does not make sense.

taple stocks are thought to be less affected by cycles and usually have lower beta. &rocter 6Damble, which makes soap, is a classic example. Lther similar ones are &hilip orris $tobacco(and *ohnson 6 *ohnson $"ealth 6 onsumer Doods(.

'+ech' stocks are commonly euated with higher beta. +his is based on experience of the dot-com bubble around year 3444. Although tech did very well in the late 1;;4s, it also fell sharply inthe early 3444s, much worse than the decline of the overall market. ore recently, this is not agood example.

Wuring the 3449 market fall, finance stocks did very poorly, much worse than the overall market.+hen in the following years they gained the most, although not to make up for their losses. +heyare still higher beta.

2oreign stocks may provide some diversification. 8orld benchmarks such as 6& Dlobal144 have slightly lower betas than comparable 5-only benchmarks such as 6& 144. "owever,this effect is not as good as it used to beN the various markets are now fairly correlated,especially the 5 and 8estern Kurope. citation needed

Werivatives and other non-linear assets. =eta relies on a linear model. An out of the moneyoption may have a distinctly non-linear payoff. +he change in price of an option relative to thechange in the price of the underlying asset $for example a stock( is not constant. 2or example, ifone purchased a put option on the 6& 744, the beta would vary as the price of the underlyingindex $and indeed as volatility, time to expiration and other factors( changed. $see options pricing,and =lackXcholes model(.

Criticismedit

https://en.wikipedia.org/wiki/United_States_Treasury_securityhttps://en.wikipedia.org/wiki/Money_market_fundhttps://en.wikipedia.org/wiki/Money_market_fundhttps://en.wikipedia.org/wiki/R_squarehttps://en.wikipedia.org/wiki/R_squarehttps://en.wikipedia.org/wiki/R_squarehttps://en.wikipedia.org/wiki/Correlationhttps://en.wikipedia.org/wiki/Procter_%26_Gamblehttps://en.wikipedia.org/wiki/Procter_%26_Gamblehttps://en.wikipedia.org/wiki/Procter_%26_Gamblehttps://en.wikipedia.org/wiki/Altria_Grouphttps://en.wikipedia.org/wiki/Johnson_%26_Johnsonhttps://en.wikipedia.org/wiki/Johnson_%26_Johnsonhttps://en.wikipedia.org/wiki/Dot-com_bubblehttps://en.wikipedia.org/wiki/Dot-com_bubblehttps://en.wikipedia.org/wiki/Dot-com_bubblehttps://en.wikipedia.org/wiki/S%26P_Global_100https://en.wikipedia.org/wiki/S%26P_Global_100https://en.wikipedia.org/wiki/S%26P_100https://en.wikipedia.org/wiki/S%26P_100https://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Options_pricinghttps://en.wikipedia.org/wiki/Options_pricinghttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=11https://en.wikipedia.org/wiki/United_States_Treasury_securityhttps://en.wikipedia.org/wiki/Money_market_fundhttps://en.wikipedia.org/wiki/R_squarehttps://en.wikipedia.org/wiki/R_squarehttps://en.wikipedia.org/wiki/Correlationhttps://en.wikipedia.org/wiki/Procter_%26_Gamblehttps://en.wikipedia.org/wiki/Procter_%26_Gamblehttps://en.wikipedia.org/wiki/Altria_Grouphttps://en.wikipedia.org/wiki/Johnson_%26_Johnsonhttps://en.wikipedia.org/wiki/Dot-com_bubblehttps://en.wikipedia.org/wiki/Dot-com_bubblehttps://en.wikipedia.org/wiki/S%26P_Global_100https://en.wikipedia.org/wiki/S%26P_Global_100https://en.wikipedia.org/wiki/S%26P_100https://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Options_pricinghttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/w/index.php?title=Beta_(finance)&action=edit&section=11


12/15

eth Ylarman of the =aupost group wrote in Margin of Safety 0


13/15

n finance, delta neutral describes a portfolio of related financial securities, in which the portfolio

value remains unchanged when small changes occur in the value of the underlying security.

uch a portfolio typically contains options and their corresponding underlying securities such that

positive and negative delta components offset, resulting in the portfolio's value being relatively

insensitive to changes in the value of the underlying security.

A related term, delta hedging is the process of setting or keeping the delta of a portfolio as close

to #ero as possible. n practice, maintaining a #ero delta is very complex because there are risks

associated with re-hedging on large movements in the underlying stock's price, and research

indicates portfolios tend to have lower cash flows if re-hedged too freuently.1

ontents

hide

• 1 @omenclature

• 3 athematical interpretation

• reating the position

• B +heory

• 7 )eferences

• O Kxternal links

$omenclat!reedit

+he sensitivity of an option's value to a change in the underlying stock's price.

+he initial value of the option.

+he current value of the option.

+he initial value of the underlying stock.

athematical interpretationedit

Main article: Greeks (finance

https://en.wikipedia.org/wiki/Financehttps://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Option_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Delta_neutral#cite_note-1https://en.wikipedia.org/wiki/Delta_neutralhttps://en.wikipedia.org/wiki/Delta_neutral#Nomenclaturehttps://en.wikipedia.org/wiki/Delta_neutral#Mathematical_interpretationhttps://en.wikipedia.org/wiki/Delta_neutral#Creating_the_positionhttps://en.wikipedia.org/wiki/Delta_neutral#Theoryhttps://en.wikipedia.org/wiki/Delta_neutral#Referenceshttps://en.wikipedia.org/wiki/Delta_neutral#External_linkshttps://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=1https://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=1https://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=2https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Financehttps://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Option_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Portfolio_(finance)https://en.wikipedia.org/wiki/Delta_neutral#cite_note-1https://en.wikipedia.org/wiki/Delta_neutralhttps://en.wikipedia.org/wiki/Delta_neutral#Nomenclaturehttps://en.wikipedia.org/wiki/Delta_neutral#Mathematical_interpretationhttps://en.wikipedia.org/wiki/Delta_neutral#Creating_the_positionhttps://en.wikipedia.org/wiki/Delta_neutral#Theoryhttps://en.wikipedia.org/wiki/Delta_neutral#Referenceshttps://en.wikipedia.org/wiki/Delta_neutral#External_linkshttps://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=1https://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=2https://en.wikipedia.org/wiki/Greeks_(finance)


14/15

Welta measures the sensitivity of the value of an option to changes in the price of the underlying

stock assuming all other variables remain unchanged.3

athematically, delta is represented as partial derivative of the option's fair value with respect

to the price of theunderlying security.

Welta is clearly a function of , however Welta is also a function of strike price and time to

expiry.

+herefore, if a position is delta neutral $or, instantaneously delta-hedged( its instantaneous

change in value, for aninfinitesimal change in the value of the underlying security, will be #eroN

see "edge $finance(. ince delta measures the exposure of a derivative to changes in the value

of the underlying, a portfolio that is delta neutral is effectively hedged. +hat is, its overall value

will not change for small changes in the price of its underlying instrument.

Creating the positionedit

Delta hedging - i.e. establishing the reuired hedge - may be accomplished by buying or selling

an amount of the underlier that corresponds to the delta of the portfolio. =y ad!usting the amount

bought or sold on new positions, the portfolio delta can be made to sum to #ero, and the portfolio

is then delta neutral. ee )ational pricing ZWelta hedging.

Lptions market makers, or others, may form a delta neutral portfolio using related optionsinstead of the underlying. +he portfolio's delta $assuming the same underlier( is then the sum of

all the individual options' deltas. +his method can also be used when the underlier is difficult to

trade, for instance when an underlying stock is hard to borrow and therefore cannot be sold

short.

Lne example of delta neutral strategy is buying a deep in the money call and buying a deep in

the money put option. Weep in the money call will have delta of 1 and deep in the money put will

have delta of -1. "ence their deltas will cancel each other to some extent of stock price

movement.

%heory edit

+he existence of a delta neutral portfolio was shown as part of the original proof of the =lackX

choles model, the first comprehensive model to produce correct prices for some classes of

options. ee =lack-choles0 Werivation.

2rom the +aylor expansion of the value of an option, we get the change in the value of an

option, , for a change in the value of the underlier 0

https://en.wikipedia.org/wiki/Delta_neutral#cite_note-2https://en.wikipedia.org/wiki/Partial_derivativehttps://en.wikipedia.org/wiki/Fair_valuehttps://en.wikipedia.org/wiki/Fair_valuehttps://en.wikipedia.org/wiki/Underlyinghttps://en.wikipedia.org/wiki/Strike_pricehttps://en.wikipedia.org/wiki/Delta_neutral#cite_note-3https://en.wikipedia.org/wiki/Infinitesimalhttps://en.wikipedia.org/wiki/Infinitesimalhttps://en.wikipedia.org/wiki/Hedge_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Hedge_(finance)https://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=3https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Rational_pricing#Delta_hedginghttps://en.wikipedia.org/wiki/Market_makerhttps://en.wikipedia.org/wiki/Stockhttps://en.wikipedia.org/wiki/Short_sellinghttps://en.wikipedia.org/wiki/Short_sellinghttps://en.wikipedia.org/wiki/Short_sellinghttps://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=4https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Derivationshttps://en.wikipedia.org/wiki/Taylor_expansionhttps://en.wikipedia.org/wiki/Delta_neutral#cite_note-2https://en.wikipedia.org/wiki/Partial_derivativehttps://en.wikipedia.org/wiki/Fair_valuehttps://en.wikipedia.org/wiki/Underlyinghttps://en.wikipedia.org/wiki/Strike_pricehttps://en.wikipedia.org/wiki/Delta_neutral#cite_note-3https://en.wikipedia.org/wiki/Infinitesimalhttps://en.wikipedia.org/wiki/Hedge_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Derivative_(finance)https://en.wikipedia.org/wiki/Hedge_(finance)https://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=3https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Rational_pricing#Delta_hedginghttps://en.wikipedia.org/wiki/Market_makerhttps://en.wikipedia.org/wiki/Stockhttps://en.wikipedia.org/wiki/Short_sellinghttps://en.wikipedia.org/wiki/Short_sellinghttps://en.wikipedia.org/w/index.php?title=Delta_neutral&action=edit&section=4https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_modelhttps://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Derivationshttps://en.wikipedia.org/wiki/Taylor_expansion


15/15

where $delta( and $gamma(N see Dreeks $finance(.

2or any small change in the underlier, we can ignore the second-order term and use the

uantity to determine how much of the underlier to buy or sell to create a hedged

portfolio. "owever, when the change in the value of the underlier is not small, the

second-order term, , cannot be ignored0 see onvexity $finance(.

n practice, maintaining a delta neutral portfolio reuires continuous recalculation of the

position's Dreeks and rebalancing of the underlier's position. +ypically, this rebalancing is

performed daily or weekly.
https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Orders_of_approximation#Second-orderhttps://en.wikipedia.org/wiki/Convexity_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)https://en.wikipedia.org/wiki/Orders_of_approximation#Second-orderhttps://en.wikipedia.org/wiki/Convexity_(finance)https://en.wikipedia.org/wiki/Greeks_(finance)

alpha beta gamma finance

Documents