RSK4805 Assignment
2 (COMPLETE
ANSWERS) 2024 - DUE
12 July 2024 ; 100%
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,Question text The volatility of an asset is 2% per day. What is the
standard deviation of the percentage price change in sixteen days?
Percentage change in price is Answer%. What extra information do
you need to calculate the covariance if you know the correlation
between two variables? standard deviation of the two variables
covariance between the asset and the market standard deviation on
only one of the variables correlation between the two variables
To calculate the standard deviation of the percentage price change in
sixteen days, given that the volatility is 2% per day, we can proceed
as follows:
1. Calculate the standard deviation of percentage price
change per day: Given volatility is 2% per day, the standard
deviation (σ) of percentage price change per day is 2%.
2. Calculate the standard deviation over sixteen days:
Standard deviation over multiple days (σ_total) is given by:
σtotal=σdaily×n\sigma_{total} = \sigma_{daily} \times
\sqrt{n}σtotal=σdaily×n
where:
o σdaily\sigma_{daily}σdaily is the daily standard
deviation (2%),
o nnn is the number of days (16).
Therefore,
σtotal=2%×16=2%×4=8%\sigma_{total} = 2\% \times
\sqrt{16} = 2\% \times 4 = 8\%σtotal=2%×16=2%×4=8%
So, the standard deviation of the percentage price change over
sixteen days is 8%8\%8%.
, Now, addressing the second part of your question:
To calculate the covariance between two variables, if you know
their correlation, you need:
• The correlation between the two variables.
The correlation coefficient (ρ) between two variables and the
standard deviations of each variable are necessary to calculate the
covariance (Cov) using the formula:
Cov(X,Y)=ρXY×σX×σY\text{Cov}(X, Y) = \rho_{XY} \times
\sigma_X \times \sigma_YCov(X,Y)=ρXY×σX×σY
where:
• ρXY\rho_{XY}ρXY is the correlation coefficient between
variables X and Y,
• σX\sigma_XσX and σY\sigma_YσY are the standard
deviations of variables X and Y, respectively.
Therefore, the extra information needed to calculate the covariance
if you know the correlation between two variables is the standard
deviation of each of the two variables involved in the correlation
calculation.
Question 2 Not yet answered Marked out of 5.00 Flag question
Question text An analyst for Bloom Ltd gathered the following
information with regards to futures contract: • Current spot-market
price of R60 • A risk-free interest rate of 8.87% per annum • The
