HW #6: Portfolio Sorts and Long-Horizon Return Inference

Student Name

Score: 0 / 8

1) Create Winner/Loser groups with `mutate()`

Use mutate() to add a new variable grp that takes on "winner" or "loser". You may want to arrange() first. Paste the code you used.

data <- tibble( stock = letters[1:10], signal = c(-.08, 0.04, 0.01, 0.12, -0.02, 0.20, 0.06, -0.10, 0.15, 0.09) ) # %>% # arrange(___) %>% # mutate(grp = if_else(___, ___, ___))

How if_else() works in R:
if_else(condition, value_if_true, value_if_false) creates a new vector. The condition must be a logical vector (TRUE/FALSE) the same length as the data. For each row: if the condition is TRUE, you get value_if_true; otherwise you get value_if_false.

2) Equal-weight Winner and Loser returns, then long-short

Compute the equal-weight Winner portfolio return and the equal-weight Loser portfolio return. Copy-paste your whole code chunk. Then compute the long-short return.

Long-short return (numeric)

3) 3-month buy-and-hold total return

Compute the 3-month buy-and-hold total return for monthly returns: 0.01, -0.02, 0.03. Use: (1+r1)(1+r2)(1+r3)-1.

4) Overlapping cohorts in February

You form a 2-month holding strategy every month: Cohort 1 forms in January (holds Jan and Feb), Cohort 2 forms in February (holds Feb and Mar), Cohort 3 forms in March (holds Mar and Apr). In February, how many cohorts are active at the same time?

5) Overlapping implies correlation (True/False)

True or False: If a strategy uses overlapping holding periods, then the strategy’s monthly returns are more likely to be correlated over time than if it used non-overlapping periods.

6) Excess and market-adjusted long-short returns

This month: long-short return \(r_{LS}=0.015\), risk-free rate \(r_f=0.002\), market return \(r_m=0.010\). Compute (1) excess long-short return \(r_{LS}-r_f\) and (2) market-adjusted long-short return \(r_{LS}-r_m\).

Excess long-short return

Market-adjusted long-short return

7) Compute the t-stat

Suppose a strategy has average monthly return \(\bar r = 0.004\) and standard error \(SE(\bar r)=0.0016\). Compute \(t=\bar r/SE(\bar r)\).

8) Time-series dependence and t-stats (dropdown)

If you ignore time-series dependence in an overlapping strategy, your t-stat is most likely to look:

# HW #6: Portfolio Sorts and Long-Horizon Return Inference

1) Create Winner/Loser groups with mutate()