Financial Toolbox For Use with MATLAB Computation Visualization Programming phần 8 ppt

Syntax [PortRisk, PortReturn, PortWts] = portoptExpReturn, ExpCovariance, NumPorts, PortReturn, ConSet Arguments Description [PortRisk, PortReturn, PortWts] = portoptExpReturn, ExpCovari

2portcons

Purpose Portfolio constraints

Syntax ConSet = portcons(varargin)

Description Using linear inequalities,portconsgenerates a matrix of constraints for a

portfolio of asset investments The matrixConSetis defined as

the value, wherePortWtsis a 1-by-number of assets (NASSETS) vector of assetallocations

parametersData1, , DataN

ConSet = portcons('ConstType1', Data11, , Data1N,'ConstType2',

constraint typesConstTypeN, and the corresponding constraint parameters

Default All allocations are >= 0; no

short selling allowed

Combined value of portfolioallocations normalized to 1

Scalar representingnumber of assets inportfolio

PVal(required) Scalarrepresenting totalvalue of portfolio

Scalar representingnumber of assets inportfolio Seepcpval

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allocation per asset

Scalar or vector oflengthNASSETS,specifying minimumallocation per asset

Scalar or vector oflengthNASSETS,specifying maximumallocation per asset

allocations to asset group

matrix specifyingwhich assets belong

to each group

Scalar or a vector oflengthNGROUPS,specifying minimumcombined allocations

in each group

Scalar or a vector oflengthNGROUPS,specifying maximumcombined allocations

in each group See

Scalar or vector oflengthNGROUPS

specifying minimumratios of allocations in

Scalar or vector oflengthNGROUPS

specifying maximumratios of allocations in

b(required) Vector oflengthNCONSTRAINTS

specifying the righthand sides of theinequalities

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Example Constrain a portfolio of three assets:

NumAssets = 3PVal = 1 % Scale portfolio value to 1

AssetMin = 0AssetMax = [0.5 0.9 0.8]

ConSet = 1.0000 1.0000 1.0000 1.0000 –1.0000 –1.0000 –1.0000 –1.0000 1.0000 0 0 0.5000

0 1.0000 0 0.9000

0 0 1.0000 0.8000 –1.0000 0 0 0

0 –1.0000 0 0

0 0 –1.0000 0 1.0000 1.0000 –1.5000 0

Portfolio weights of 30% in IBM, 30% in CPQ, and 40% in XON satisfy theconstraints

See Also pcalims, pcgcomp, pcglims, pcpval, portopt

2portopt

Purpose Portfolios on constrained efficient frontier

Syntax [PortRisk, PortReturn, PortWts] = portopt(ExpReturn, ExpCovariance,

NumPorts, PortReturn, ConSet)

Arguments

Description [PortRisk, PortReturn, PortWts] = portopt(ExpReturn, ExpCovariance,

frontier with user-specified covariance, returns, and asset constraints

asset investment weights that minimize the risk for given values of theexpected return The portfolio risk is minimized subject to constraints on thetotal portfolio value, the individual asset minimum and maximum allocation,the asset group minimum and maximum allocation, or the asset

group-to-group comparison

portfolio

expected (mean) return of each asset

of the asset returns

frontier Returns are equally spaced between themaximum possible return and the minimum riskpoint IfNumPortsis empty (entered as[]),computes

10equally spaced points

portfolios (NPORTS)-by-1vector If not entered or empty,

minimum and maximum possible values are used

created usingportcons If not specified, a default iscreated

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Each row represents a portfolio The total of all weights in a portfolio is 1

efficient frontier

Examples Plot the risk-return efficient frontier of portfolios allocated among three assets

Connect 20 portfolios along the frontier having evenly spaced returns Bydefault, choose among portfolios without short-selling and scale the value ofthe portfolio to 1

ExpReturn = [0.1 0.2 0.15];

ExpCovariance = [ 0.005 -0.010 0.004 -0.010 0.040 -0.002 0.004 -0.002 0.023 ];

NumPorts = 20;

portopt(ExpReturn, ExpCovariance, NumPorts)

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.12

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2

0.21

Mean−Variance−Efficient Frontier

Risk(Standard Deviation)

Return the two efficient portfolios that have returns of 16% and 17% Limit toportfolios that have at least 20% of the allocation in the first asset, and cap thetotal value in the first and third assets at 50% of the portfolio

ExpReturn = [0.1 0.2 0.15];

ExpCovariance = [ 0.005 -0.010 0.004 -0.010 0.040 -0.002 0.004 -0.002 0.023 ];

PortReturn = [0.16 0.17];

[PortRisk, PortReturn, PortWts] = portopt(ExpReturn,

ExpCovariance, [], PortReturn, ConSet)PortRisk =

0.0919 0.1138PortReturn =

0.1600 0.1700 PortWts = 0.3000 0.5000 0.2000 0.2000 0.6000 0.2000

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2portrand

Purpose Randomized portfolio risks, returns, and weights

Syntax [risk, ror, weights] = portrand(asset, ret, pts)

[risk, ror, weights] = portrand(asset, ret)[risk, ror, weights] = portrand(asset)portrand(asset, ret, pts)

Arguments asset M-by-N matrix of time series data Rows (M) are observations, and

each column (N) represents a single security

ret 1-by-N vector where each column represents the rate of return for the

corresponding security inasset By default,retis computed by takingthe average value of each column ofasset

pts Scalar that specifies how many random points should be generated

Default =1000

Description [risk, ror, weights] = portrand(asset, ret, pts) returns the risks,

rates of return, and weights of random portfolio configurations

risk Apts-by-1 vector of standard deviations

ror Apts-by-1 vector of expected rates of return

different portfolio configuration

configuration It does not return any data to the MATLAB workspace

This function is used in the MATLAB Financial Expo and illustrates howmultiple weighting combinations of the same portfolio will generate the sameexpected rate of return

See Also frontier

Reference Bodie, Kane, and Marcus, Investments, Chapter 7.

2portsim

Purpose Random simulation of correlated asset returns

Syntax RetSeries = portsim(ExpReturn, ExpCovariance, NumObs, RetIntervals,

NumSim)

Arguments

Description portsim simulates returns ofNASSETSassets over consecutive observation

intervals Returns are simulated as the increments of constant drift andvolatility Brownian processes

observations The return over an interval of lengthDTis given by

scalar whose value changes each timerandnis referenced

The returns realized from portfolios listed inPortWtsare given by:

which each row contains the asset allocations of a portfolio Each row of

column corresponds to one of the observations inRetSeries Seeportoptand

expected (mean) return of each asset

covariances The standard deviations of the returns

series IfNumObsis entered as the empty matrix[], thelength ofRetIntervalsis used

of interval times between observations If

assumed to have length 1

observations to perform Default = 1

NumObs = 10;

RetSeries = portsim(ExpReturn, ExpCovariance, NumObs)RetSeries =

0.1429 0.2626 0.2365 0.0821 0.1599 –0.1796 0.0054 0.6126 0.1072 0.1719 –0.0669 0.1913 0.1518 –0.0843 0.0442 0.0112 0.2709 0.1501 0.0409 0.1683 0.1932 0.1485 0.2522 0.2774 0.0463 0.3222 0.0954 0.1990 0.1024 0.3843

See Also ewstats,portopt,portstats,randn,ret2tick

2portstats

Purpose Portfolio expected return and risk

Syntax [PortRisk, PortReturn] = portstats(ExpReturn, ExpCovariance,

PortWts)

Arguments

Description [PortRisk, PortReturn] = portstats(ExpReturn, ExpCovariance,

assets

expected (mean) return of each asset

of the asset returns

weights allocated to each asset Each row represents adifferent weighting combination Default =1/NASSETS

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Examples ExpReturn = [0.1 0.2 0.15];

ExpCovariance = [ 0.0100 –0.0061 0.0042 –0.0061 0.0400 –0.0252 0.0042 –0.0252 0.0225 ];

PortWts=[0.4 0.2 0.4; 0.2 0.4 0.2];

[PortRisk, PortReturn] = portstats(ExpReturn, ExpCovariance, PortWts)

PortRisk = 0.0560 0.0550PortReturn = 0.1400 0.1300

See Also frontcon

2portvrisk

Purpose Portfolio value at risk

Syntax ValueAtRisk = portvrisk(PortReturn, PortRisk, RiskThreshold,

PortValue)

Arguments

Description ValueAtRisk = portvrisk(PortReturn, PortRisk, RiskThreshold,

one period of time, given the loss probability levelRiskThreshold

portfolio, predicted with a confidence probability of1– RiskThreshold

0.0688 0.0478 0.0366

the expected return of each portfolio over the period

of each portfolio over the period

probability Default =0.05(5%)

of asset portfolio Default =1

1.0e+007 * 3.6572 1.8684

See Also frontcon,portopt

2prbond

Purpose Price of security with regular periodic interest payments

Syntax [p, ai] = prbond(sd, md, rv, cpn, yld, per, basis)

[p, ai] = prbond(sd, md, rv, cpn, yld, per)[p, ai] = prbond(sd, md, rv, cpn, yld)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

rv Redemption (par, face) value

cpn Coupon rate Enter as decimal fraction

yld Yield Enter as decimal fraction

per Coupons per year An integer Default =2

2= actual/360,3= actual/365

Description [p, ai] = prbond(sd, md, rv, cpn, yld, per, basis) returns the price

pand accrued interestaiof a security with regular periodic interest payments.This function also applies to zero-coupon bonds or pure discount securities bysettingcpn = 0

Example Using this data:

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returns

p = 1276.64e+003

ai = 6.8132

See Also acrubond, prdisc, prmat, proddf, proddfl, proddl, yldbond

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formulas 6, 7

2prdisc

Purpose Price of discounted security

Syntax p = prdisc(sd, md, rv, disc, basis)

p = prdisc(sd, md, rv, disc)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

rv Redemption (par, face) value

disc Discount rate of the security Enter as decimal fraction

See Also acrudisc, prbond, prmat, ylddisc

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formula 2

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2prmat

Purpose Price with interest at maturity

Syntax [p, ai] = prmat(sd, md, id, rv, cpn, yld, basis)

[p, ai] = prmat(sd, md, id, rv, cpn, yld)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

id Issue date Enter as serial date number or date string

rv Redemption (par, face) value

cpn Coupon rate Enter as decimal fraction

yld Yield Enter as decimal fraction

2= actual/360,3= actual/365

Description [p, ai] = prmat(sd, md, id, rv, cpn, yld, basis) returns the pricep

and accrued interestaiof a security that pays interest at maturity Thisfunction also applies to zero-coupon bonds or pure discount securities bysettingcpn = 0

Example Using this data:

returns

p = 99.9784

ai = 1.9591

See Also acrubond, acrudisc, prbond, prdisc, yldmat

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formula 4

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2proddf

Purpose Price with odd first period

Syntax [p, ai] = proddf(sd, md, id, fd, rv, cpn, yld, per, basis)

[p, ai] = proddf(sd, md, id, fd, rv, cpn, yld, per)[p, ai] = proddf(sd, md, id, fd, rv, cpn, yld)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

id Issue date Enter as serial date number or date string

fd First coupon date Enter as serial date number or date string

rv Redemption (par, face) value

cpn Coupon rate Enter as decimal fraction

yld Yield Enter as decimal fraction

per Coupons per year An integer Default =2

2= actual/360,3= actual/365

Description [p, ai] = proddf(sd, md, id, fd, rv, cpn, yld, per, basis) returns

the pricepand accrued interestaiof a security with an odd first period and thesettlement date in the first period

Example Using this data:

returns

p = 113.5977

ai = 0.5855

See Also acrubond, cfdates, prbond, proddfl, proddl, yldoddf

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formulas 8, 9

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2proddfl

Purpose Price with odd first and last periods and settlement in first period

Syntax [p, ai] = proddfl(sd, md, id, fd, lcd, rv, cpn, yld, per, basis)

[p, ai] = proddfl(sd, md, id, fd, lcd, rv, cpn, yld, per)[p, ai] = proddfl(sd, md, id, fd, lcd, rv, cpn, yld)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

id Issue date Enter as serial date number or date string

fd First coupon date Enter as serial date number or date string

lcd Last coupon date Enter as serial date number or date string

rv Redemption (par, face) value

cpn Coupon rate Enter as decimal fraction

yld Yield Enter as decimal fraction

per Coupons per year An integer Default =2

2= actual/360,3= actual/365

Description [p, ai] = proddfl(sd, md, id, fd, lcd, rv, cpn, yld, per, basis)

returns the pricepand accrued interestaiof a security with odd first and lastperiods and the settlement date in the first period

ai = 0.1556

See Also acrubond, cfdates, prbond, proddf, proddl, yldbond, yldoddfl

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formulas 16, 17, 18, 19

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2proddl

Purpose Price with odd last period

Syntax [p, ai] = proddl(sd, md, lcd, rv, cpn, yld, per, basis)

[p, ai] = proddl(sd, md, lcd, rv, cpn, yld, per)[p, ai] = proddl(sd, md, lcd, rv, cpn, yld)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

lcd Last coupon date Enter as serial date number or date string

rv Redemption (par, face) value

cpn Coupon rate Enter as decimal fraction

yld Yield Enter as decimal fraction

per Coupons per year An integer Default =2

2= actual/360,3= actual/365

Description [p, ai] = proddl(sd, md, lcd, rv, cpn, yld, per, basis) returns the

pricepand accrued interestaiof a security with odd last period

Example Using this data:

returns

p = 100.5411

ai = 0.0542

See Also acrubond, cfdates, prbond, proddf, proddfl, yldoddl

Reference Mayle, Standard Securities Calculation Methods, Volumes I-II, 3rd edition.

Formulas 11, 13, 14, 15

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2prtbill

Purpose Price of Treasury bill

Syntax p = prtbill(sd, md, rv, disc)

Arguments sd Settlement date Enter as serial date number or date string sdmust

be earlier than or equal tomd

md Maturity date Enter as serial date number or date string

rv Redemption (par, face) value

disc Discount rate of the Treasury bill Enter as decimal fraction

Description p = prtbill(sd, md, rv, disc) returns the pricepfor a Treasury bill

Example The settlement date of a Treasury bill is February 10, 1992, the maturity date

is August 6, 1992, the discount rate is 3.77%, and the par value is $1000 Usingthis data:

p = prtbill('2/10/1992', '8/6/1992', 1000, 0.0377)

returns

p = 981.3594

See Also beytbill, yldtbill

Reference Bodie, Kane, and Marcus, Investments, pages 41-43.