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Coursework 2. Cohort 2023/24. This assignment is worth 60% of the overall mark.
All reports will be checked for plagiarism and plagiarism cases will be thoroughly investigated, do not include non-original material (text, images, tables) without clearly stating the source.
Standard and non-standard calculators are permitted
1. Time Series Prep [30 Points]
(a) Download SPTL ETF (1
) at end-of-day prices for the period of time between 1 Jan 2014 to 31 December 2019. Download the Effective Fed Funds Rate (EFFR Index) 2
as the risk-free rate. Adjust annual risk-free rate to make it a daily rate, i.e., rt
f = EF F R(t) · dc, where dc is a day-count. You can use dc ≈ (1/252).
A unit of SPTL will cost pt at time t, which we have to finance at the risk-free rate.
The daily excess return per unit of SPTL reads,
(b) Plot the SPTL return time series, the EFFR, and the excess return per unit of SPTL,
starting from t = 0 corresponding to 1 Jan 2014.
2. Trading Strategies [45 Points]
Definition. In a leveraged strategy, the (leveraged) book size is the available capital times the leverage amount. By a leveraged strategy we mean a sequence {θt}
T
t=1 of dollar values of SPTL which can be long or short such that where V0 is the initial capital, and L is the leverage.
(a) Define three leveraged trading strategies for the SPTL with initial capital V0 = $200, 000. For all strategies, set the leverage L = 10. Use the first 70% of days as training set and the remaining 30% as test set. The daily trading PnL, which we define as the excess return of each strategy {θt}
T t=1, is given by the equation:
where θt
is the dollar value of SPTL held at time t (i.e., θt = units(t) × pt).
(b) Plot the position of the strategies θt
together with the upper and lower bounds [−Vt
· L, Vt
· L]. Calculate the turnover in dollar value traded over time
