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Assuming that the returns distribution of a portfolio is normal, using the parametric method
of estimation of VaR needs which of the following inputs:
A) mean, standard deviation and size of the lookback period.
B) mean and standard deviation.
C) mean, standard deviation, and kurtosis.
Ryan Manning is a new hire at Luongo Asset Managers. As part of his training, he has been
asked to compile a report on risk measurement and mechanisms to control risk.
Manning wants to give a simple illustration of VaR and has compiled the data for a two-asset
portfolio as shown in Exhibit 1.
Exhibit 1:
Weighting
Asset
Daily standard
deviation
Average daily
return
Standard deviation of
daily return
70%
Wszolek
plc
0.0186
0.06%
1.54
30%
Sylla plc
0.0124
0.04%
Current market value of portfolio £7,500,000
Manning's colleague, Alex Smith, makes three comments about Manning's computation of
VaR:
Comment
1:
"VaR is such a useful measure as it shows us the maximum potential loss on
our portfolio position. Your data shows the maximum daily loss that could be
incurred 5% of the days."
Comment
2:
"When using a parametric approach great care needs to be taken with the
look-back period. The raw data should only really be used if the historic
parameter estimates are similar to what we are expecting over the period for
which we are estimating VaR."
Manning's report contains a discussion on the historical simulation method of estimating
VaR. Manning states:
"The historical simulation approach to VaR is based on the actual periodic changes in risk
factors over a look-back period. The daily change in value of the portfolio is calculated for
each day over the look-back period. We then order the changes from most positive to most
negative and look for the largest 5% of losses. The VaR is then the average of the 5% biggest
losses. One advantage it has is that it doesn't use normal distributions and as a result can be
used for portfolios containing options."
Manning's report contains three limitations of VaR:
Limitation
1:
If VaR is calculated under the assumption of normal distributions of asset
returns, it will often underestimate the severity of losses. One cause of this is
platykurtic return distributions.
Limitation
2:
During periods of financial distress asset correlations will often increase. This
means that computing VaR based on historical correlations observed over a
look-back period might well overestimate the benefits of diversification and as
a result underestimate the magnitude of potential losses.
Limitation
3:
VaR computation does not account for the liquidity of assets in its calculation.
When asset prices fall dramatically, liquidity often dissipates significantly as
was seen with asset-backed securities during the credit crunch of 2008–2009.
This has means that VaR will underestimate the true losses of liquidating
positions that are under extreme price pressure.