ECON 6070代做、data代写、代做Java，Python，c/c++程序语言

日期：2020-05-20 10:28

Pset 2, ECON 6070

A. Factor models.

The data contains all firms traded from 1989-2015. This problem set is due on May

18th.

1. Read data from cleaned data.csv and FF-5 factors. match the dates from 1989

on monthly basis. Drop those firms if there is any missing data.

2. For each stock i and time t, consider the following factor regression:

Rit = αi + βift + it. Estimate the model using the first 80% of data (aka training

sample )and leave the rest 20% as the testing data.

Report the mean and standard deviation of ˆα across i = 1, 2, ..., N, where N is the

total number of stocks. Report the average in sample R2 and out of sample R2 over i.

3. Consider the Markowitz optimal portfolio w =1γΣ−1

(µ−re), where e = (1, 1, ..., 1)0

is a N × 1 vector of ones. Let γ = 2 and risk free rate r = 1%.

Compute ˆµ and Σ from the training sample based on the factor model: ˆ ˆ µi:= ˆαi +βˆiEn[fit] for i = 1, 2, ..., N, and V ar(Rt) = BV ar d (ft)B0+diag(ˆσ21, ..., σˆ2N ), where V ar d (ft)

is the sample covariance matrix of ft, and ˆσ2i:= 1T −p

PTt=1 ˆ2it, ˆit := Rit − αˆi − βˆift, and

p is the number of factors.

Report: (a) the return and volatility of the plug in optimal portfolio ˆw := 1γΣˆ −1(ˆµ −re) in the training sample.

(b) the return and volatility of the plug in optimal portfolio ˆw := 1γΣˆ −1(ˆµ − re) in

the testing sample. Do you see any differences between (a) and (b)?

B. Simulations and Black-Scholes

Consider a law of motion of returns: rt+1 := α + βrt + t, where α = 0.04, β = 0.8,and t ∼ N(0, σ2), σ = 20%. Initial price P0 = 100. Set r0 = 0.

There is an call option with a strike price K and a maturity T = 10.

Simulate M = 500 price paths from t = 0 to t = T and obtain 500 ”simulated price

at maturity” P1T, ..., P MT.

Compute the “NPV” valuation of the option Cˆ(K) := 1M1(1+r)

TPM

i=1 max(0, PiT −K).

Report a table of Cˆ(K) with K = 100, 120, 140, 160, 180, 200.

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