The relationship between South
Date
2011-03-30
Authors
Comline, Mark
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Abstract
The volatility of a share or market is used as a proxy for risk in a number of
financial calculations. Volatility measures the deviation from the average value, and
is therefore an estimate of how much a share or market moves up and down. It is
therefore measured as the standard deviation, or the square root of the variance of
a time series. Understanding time-varying volatility of the South African stock and
bond market, as well as that of the US stock market, is of interest to fund
managers, and can have an effect on portfolio selection.
The background to the individual markets, volatility in general, and findings of
volatility of other stock and bond markets are discussed. Volatility of one market is
described as having an influence on another market, through what is termed
volatility transmission. Therefore a time-varying covariance between the markets
can be determined, which assists in the description of the relationship between the
respective markets’ volatility.
This research describes the relationship between the volatility of the South African
stock and bond market and the US stock market, through determination of a timevarying
variance-covariance matrix of the markets. This is performed through the
framework of a GARCH(1,1) model with BEKK representation for the variancecovariance
matrix (Engle and Kroner 1995). Further restrictions are placed on
elements of the model to allow empirical determination of causality in variance in
one direction at a time, for example from stock to bond market, and from bond to
stock market. The relationship is therefore determined within a framework that
allows for prediction of the variance and covariance conditional on previous existing
information.
Results from this research indicate that the South African stock, bond and US stock
markets are highly persistent on themselves. Results further indicate that volatility
is transmitted in a unidirectional manner from the South African stock market to the
South African bond market. The influence of volatility transmission is seen from the
volatility persistence value, or the previous days’ stock market volatility, causing a
negative influence on the current day’s bond market variance level. There is no
significant influence of the South African bond market volatility on the volatility of
the stock market.
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There is no evidence of a volatility relationship between the South African bond
market and the US stock market. The US stock market, however, is determined to
have a bidirectional volatility transmission relationship with the South African stock
market. The volatility is transmitted through shocks in one market influencing the
volatility of the other market, as well as through changes in the persistence of one
market influencing the volatility of the other market. The US stock market is
identified as the dominant partner in the relationship, as the magnitude of the
volatility transmission from the US stock market to the South African stock market
is larger than the volatility linkage in the opposite direction.
Description
MBA - WBS
Keywords
Stocks and bonds, Stock volatility