N1569 Workshop 3
Calculation Questions
1. What is the expected return of this portfolio?
• Asset A: Weight = 40%, expected return = 9%
• Asset B: Weight = 40%, expected return = 6%
• Asset C: Weight = 20%, expected return = 12%
2. Calculate the covariance between A and B where:
• Standard deviation of Asset A = 18%
• Standard deviation of Asset B = 12%
• Correlation between A and B = 0.7
3. Based on daily data of realised returns, the mean return is 0.02% and the standard deviation of returns is 1.2%. Assuming 250 trading days per year, find the annualized mean return and volatility.
4. What is the risk contribution of Asset A to the portfolio volatility?
• Asset A: Weight = 60%, Volatility = 20%
• Asset B: Weight = 40%, Volatility = 25%
• Correlation between A and B = 0.4
Excel Exercises
A. Uni.xls contains historical prices of the Uniswap decentralized exchange token (UNI).
(i) Upload the spreadsheet to ChatGPT’s Excel AI and ask it to draw a time series graph of the UNI token prices.
(ii) Use the Excel formula bar to calculate the daily log and realised returns, take their difference and plot this as a time series graph in Excel, commenting on the result
B. A portfolio contains five stocks, A, B, C and D with holdings worth $4m, $2m, $5m, $4m and $5m respectively. Their volatilities 20%, 30%, 25%, 15% and 10% respectively and their returns all have pairwise correlation 0.5.
(i) Enter the holding values as a column in Excel and then produce another 5 ×1 column vector w next to it containing the portfolio weights
(ii) Enter their volatilities into a 5 × 5 diagonal matrix D and their correlations into a 5 × 5 matrix C
(iii) Use the MMULT function to compute the covariance matrix as V = DCD
(iv) Use the MMULT function to compute the portfolio variance as w′ Vw and then take the square root to find the portfolio volatility
(v) Explore how this volatility changes with the correlations between the stock returns