Monte Carlo simulation of correlated asset returns
RetSeries = portsim(ExpReturn,ExpCovariance,NumObs,RetIntervals,NumSim,Method
)
 1 by number of assets ( 


 Positive scalar integer indicating the number of consecutive
observations in the return time series. If 
 (Optional) Positive scalar or number of observations

 (Optional) Positive scalar integer indicating the number
of simulated sample paths (realizations) of 
 (Optional) Character vector indicating the type of Monte Carlo simulation:
For either method, the sample mean and
covariance returned are appropriately scaled by 
portsim
simulates correlated returns of NASSETS
assets
over NUMOBS
consecutive observation intervals.
Asset returns are simulated as the proportional increments of constant
drift, constant volatility stochastic processes, thereby approximating
continuoustime geometric Brownian motion.
RetSeries
is a NUMOBS
byNASSETS
byNUMSIM
threedimensional
array of correlated, normally distributed, proportional asset returns.
Asset returns over an interval of length dt are
given by
$$\frac{dS}{S}=\mu dt+\sigma dz=\mu dt+\sigma \epsilon \sqrt{dt},$$
where S is the asset price, μ is the expected rate of return, σ is the volatility of the asset price, and ε represents a random drawing from a standardized normal distribution.
When Method
is 'Exact'
,
the sample mean and covariance of all realizations (scaled by RetIntervals
)
match the input mean and covariance. When the returns are then converted
to asset prices, all terminal prices for a given asset are in close
agreement. Although all realizations are drawn independently, they
produce similar terminal asset prices. Set Method
to 'Expected'
to
avoid this behavior.
The returns from the portfolios in PortWts
are
given by PortReturn = PortWts * RetSeries(:,:,1)'
, where PortWts
is
a matrix in which each row contains the asset allocations of a portfolio.
Each row of PortReturn
corresponds to one of the
portfolios identified in PortWts
, and each column
corresponds to one of the observations taken from the first realization
(the first plane) in RetSeries
. See portopt
and portstats
for
portfolio specification and optimization.
Hull, John, C. Options, Futures, and Other Derivatives. 5th Edition. Upper Saddle River, New Jersey: PrenticeHall, 2003, ISBN 0130090565.