,Q1 Suppose that each of two investments has a 4% chance of a
loss of R15 million, a 1% chance of a loss of R1.5 million and a
95% chance of a profit of R1.5 million. They are independent of
each other. Calculate the expected shortfall (ES) when the
confidence level is 95%? The expected shortfall for one of the
investments is the expected loss conditional that the loss is in the
5% tail. Given that we are in the tail, there is a Answer %
chance than the loss is R1.5 million and an Answer % chance
that the loss is R15 million. The expected loss is equal to R
Answer million. Round your answer to two decimal places (e.g.,
10.15 million)
To calculate the expected shortfall (ES) when the confidence
level is 95% for the two independent investments, follow these
steps:
1. Determine the Distribution of Losses
Each investment has the following probabilities:
• 4% chance of a loss of R15 million
• 1% chance of a loss of R1.5 million
• 95% chance of a profit of R1.5 million
2. Calculate the Expected Shortfall (ES) for One Investment
, The expected shortfall at the 95% confidence level is the
expected loss given that the loss is in the worst 5% of outcomes.
For one investment:
• Probability of Losses:
o Probability of R15 million loss = 4% (0.04)
o Probability of R1.5 million loss = 1% (0.01)
o Probability of Profit = 95% (0.95)
In the tail (the worst 5%):
• Total probability of losses = 4% + 1% = 5%
Given that we are in the tail, we need to calculate the proportion
of the tail losses:
• Probability of R15 million loss given tail =
4%5%=80%\frac{4\%}{5\%} = 80\%5%4%=80%
• Probability of R1.5 million loss given tail =
1%5%=20%\frac{1\%}{5\%} = 20\%5%1%=20%
Expected loss in the tail:
Expected loss=(0.80×15 million)+(0.20×1.5 million)\text{Expec
ted loss} = (0.80 \times 15 \text{ million}) + (0.20 \times 1.5
\text{
million})Expected loss=(0.80×15 million)+(0.20×1.5 million)
Expected loss=12 million+0.30 million\text{Expected loss} =
12 \text{ million} + 0.30 \text{
million}Expected loss=12 million+0.30 million
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