CONFIDENTIAL DSC3705 7 Oct/Nov 2023
OCTOBER/NOVEMBER 2023
DSC3705
Financial Risk Modelling
Duration: 3 hours 75 marks
Question 1 3
An investor’s total wealth is R50000 and he wants to invest in a portfolio with securities D, E and F, with expected
returns E[rD] = 20%, E[rE] = 15% and E[rF] = 17% respectively. If he chooses to invest R25000 in security D,
R12500 in security E and R12500 in security F, what will be the expected return of this portfolio?
Question 2 2
Consider a portfolio of risky equities and Treasury bills. Suppose the expected return on equities is 12%, with a
volatility of 18%. Assume that Treasury bills o er a risk-free rate of 7%. Determine the volatility of the portfolio
if 60% is invested in equities and 40% is invested in Treasury bills.
To find the expected return of the portfolio when investing in multiple securities, you can use a
weighted average of the expected returns of each security based on the amount invested in
each security. The formula for the expected return of a portfolio is:
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, CONFIDENTIAL DSC3705 7 Oct/Nov 2023
Question 3 3
Briefy explain the dierence between beta as a measure of risk and volatility as a measure of risk.
Beta and volatility are both measures of risk in the context of investments, but they capture different aspects
of risk and have distinct interpretations:
Beta:
Page 2 of 23
, CONFIDENTIAL DSC3705 7 Oct/Nov 2023
Beta measures a security's sensitivity to overall market movements. It indicates how much a particular asset's
returns tend to move in relation to the returns of the broader market, typically represented by a benchmark
index like the S&P 500.
A beta of 1 means the asset tends to move in sync with the market. A beta greater than 1 indicates the asset is
more volatile than the market, and a beta less than 1 suggests it is less volatile.
Beta is used to assess systematic risk, which is risk that cannot be eliminated through diversification. It helps
investors understand how a particular asset will likely perform in relation to the overall market.
Volatility:
Volatility, often measured using metrics like standard deviation, reflects the degree of variation or fluctuations
in the price or returns of an asset over time. High volatility implies that the asset's returns can vary widely from
their average, while low volatility suggests more stability.
Volatility measures the total risk of an asset, including both systematic (market-related) and unsystematic
(asset-specific) risk. It doesn't consider the asset's relationship with the broader market, as beta does.
Investors often use volatility as a risk measure to assess the potential for significant price swings, which can
impact their investment's stability and predictability.
In summary, beta primarily assesses an asset's risk in relation to the market, focusing on systematic risk, while
volatility assesses the overall variability in an asset's returns, encompassing both systematic and unsystematic
Page 3 of 23
OCTOBER/NOVEMBER 2023
DSC3705
Financial Risk Modelling
Duration: 3 hours 75 marks
Question 1 3
An investor’s total wealth is R50000 and he wants to invest in a portfolio with securities D, E and F, with expected
returns E[rD] = 20%, E[rE] = 15% and E[rF] = 17% respectively. If he chooses to invest R25000 in security D,
R12500 in security E and R12500 in security F, what will be the expected return of this portfolio?
Question 2 2
Consider a portfolio of risky equities and Treasury bills. Suppose the expected return on equities is 12%, with a
volatility of 18%. Assume that Treasury bills o er a risk-free rate of 7%. Determine the volatility of the portfolio
if 60% is invested in equities and 40% is invested in Treasury bills.
To find the expected return of the portfolio when investing in multiple securities, you can use a
weighted average of the expected returns of each security based on the amount invested in
each security. The formula for the expected return of a portfolio is:
Page 1 of 23
, CONFIDENTIAL DSC3705 7 Oct/Nov 2023
Question 3 3
Briefy explain the dierence between beta as a measure of risk and volatility as a measure of risk.
Beta and volatility are both measures of risk in the context of investments, but they capture different aspects
of risk and have distinct interpretations:
Beta:
Page 2 of 23
, CONFIDENTIAL DSC3705 7 Oct/Nov 2023
Beta measures a security's sensitivity to overall market movements. It indicates how much a particular asset's
returns tend to move in relation to the returns of the broader market, typically represented by a benchmark
index like the S&P 500.
A beta of 1 means the asset tends to move in sync with the market. A beta greater than 1 indicates the asset is
more volatile than the market, and a beta less than 1 suggests it is less volatile.
Beta is used to assess systematic risk, which is risk that cannot be eliminated through diversification. It helps
investors understand how a particular asset will likely perform in relation to the overall market.
Volatility:
Volatility, often measured using metrics like standard deviation, reflects the degree of variation or fluctuations
in the price or returns of an asset over time. High volatility implies that the asset's returns can vary widely from
their average, while low volatility suggests more stability.
Volatility measures the total risk of an asset, including both systematic (market-related) and unsystematic
(asset-specific) risk. It doesn't consider the asset's relationship with the broader market, as beta does.
Investors often use volatility as a risk measure to assess the potential for significant price swings, which can
impact their investment's stability and predictability.
In summary, beta primarily assesses an asset's risk in relation to the market, focusing on systematic risk, while
volatility assesses the overall variability in an asset's returns, encompassing both systematic and unsystematic
Page 3 of 23
