Risky Weights

Group Name:

Student Name	Student Number
1:
2:
3:
4:
5:

This is an assignment. You may work in groups. Please write your group and group member names above. You will find sections labeled Task asking you to do each piece of analysis. Please make sure that you complete all of these tasks. I included some tests to help you see if you are calculating the solution correctly, but if you cannot get the test to pass submit your best attempt and you may recieve partial credit.

All work that you submit should be your own. Make use of the course resources and example code on the course website. It should be possible to complete all the requested tasks using information given below or somewhere on the course website.

#r "nuget: FSharp.Data, 5.0.2"
#r "nuget: FSharp.Stats, 0.5.0"
#r "nuget: Quotes.YahooFinance"
#r "nuget: Plotly.NET, 3.*"

open System
open FSharp.Data
open Plotly.NET
open FSharp.Stats
open Quotes.YahooFinance

for testing.

#r "nuget: FsUnit.Xunit"
#r "nuget: xunit, 2.*"
open Xunit
open FsUnit.Xunit
open FsUnitTyped

Load Data

We get the SPY ETF

type MonthlyReturn = { Date: DateTime; Return: float }
let spy = 
    YahooFinance.History("SPY", 
                         startDate = DateTime(2010,1,1), 
                         endDate = DateTime(2023, 2, 28),
                         interval = Monthly)
    |> List.sortBy (fun month -> month.Date)
    |> List.pairwise
    |> List.map (fun (m0, m1) -> 
        { Date = m1.Date
          Return = (m1.AdjustedClose - m0.AdjustedClose) / m0.AdjustedClose })

Load risk-free rate

// 4-week Treasury Bill: Secondary Market Rate
type DTB4WK = CsvProvider<"https://fred.stlouisfed.org/graph/fredgraph.csv?id=DTB4WK",
                           Schema="Date,RiskFreeRate (float)",
                           MissingValues=".">


// We'll take the 4-week interest rate at the start of the month as the risk-free rate for that month.
// Then we'll put it in a dictionary for efficient lookup.
let rf =
    DTB4WK.GetSample().Rows
    |> Seq.toList
    |> List.filter (fun x -> not (Double.IsNaN x.RiskFreeRate))
    |> List.groupBy (fun day -> day.DATE.Year, day.DATE.Month)
    |> List.map (fun (month, daysInMonth) ->
        let firstDay = 
            daysInMonth 
            |> List.sortBy (fun day -> day.DATE)
            |> List.head
        let date = DateTime(firstDay.DATE.Year, firstDay.DATE.Month, 1)
        // discount basis assumes 30 days in a month, 360 days per year.
        let ret = (30.0 / 360.0) * firstDay.RiskFreeRate / 100.0 
        date, ret)
    |> dict

Look at an example, the index is date

rf[DateTime(2010,1,1)]

Calculating excess returns of spy returns:

let excessSpy =
    [ for x in spy do 
        { Date = x.Date
          Return = x.Return - rf.[x.Date] } ]

As an example, I'll first calculate the standard deviation of the the excess returns of SPY and assign it to a value named stdDevExcessSpy.

let stdDevExcessSpy =
    excessSpy
    |> stDevBy (fun x -> x.Return)

The following test will pass if I calculate it correctly.

// Test.
stdDevExcessSpy
|> should (equalWithin 0.005) 0.04

The test following test will fail if I calculate it incorrectly. In this failing example I report an annualized standard deviation instead of a monthly standard deviation.

let stdDevFAIL =
    let monthlyStDev = 
        excessSpy
        |> stDevBy (fun x -> x.Return)
    monthlyStDev * (sqrt 12.0)

// Test
if false then // make this `if true` to run the test.
    stdDevFAIL
    |> should (equalWithin 0.005) 0.04