3FH3 Fall 2024 Problem Set 2

Java Python 3FH3 Fall 2024

Problem Set 2

100 points total

Instructions:

Include your answers and code and upload them to the A2L Dropbox.

-    If you are using Colab, either write everything in one “.ipynb” file, or write separately into a pdf file and “.ipynb” file.

-    If you are using Excel, include both your write-up and spreadsheets. 

The due date is November 3 at 11:59 PM.

1.   Book Value, Investment, and Market Value (20 points) Consider the following two equity-only firms:

-    Firm A and Firm B both have a starting book value of $1000.

-    Both firms have a fixed ROA of 20%.

-    Firm A is going to distribute all its earnings as dividends to equity investors, while Firm B always retains 50% of the earnings.

-    Both Firm A and B have a discount rate of 10%.

-    Both firms are to live for 10 years. At the end of year 10, both firms are going to liquidate the firm at face value.

-    Assume no tax or depreciation.

-    Hint: first, work out the growth rate for book value and earnings using ROA and payout ratio.

Compute the intrinsic values for both Firm A and B. Briefly explain why they are different.

2.   Fundamental Valuation (30 points)

Use Yahoo Finance data to value the stock price of “GOOGL”. Download (or copy) the “Financials” and “Historical Data” from Yahoo Finance page of “GOOGL” .

a.   Free cash flow to equity. Compute per share FCFE for each of the 4 years. (10 points)

b.  Now go to historical data and download monthly stock prices from 1/1/2011 to 12/31/2023 for both “GOOGL” and “SPY” . Use “adjusted close” to compute monthly returns for both “GOOGL” and “SPY” . Run a simple regression of “GOOGL” returns on “SPY” to find the # of “GOOGL.” Suppose the long-run risk-free rate is 1%, and the equity market risk premium is 6%. What is the estimated cost of equity fo 3FH3 Fall 2024 Problem Set 2 r “GOOGL” according to CAPM? (10 points)

c.   Now suppose you stand at the end of 2023 and are ready to project GOOGL

earnings into the future. You consider GOOGL to be still innovative to have the  next 10 years growing at a relatively fast pace. Use the average per share FCFE growth rate in the past 3 years as first-stage growth rate. After 10 years, you assume GOOGL’s FCFE is going to grow by 2% forever. Compute the intrinsic value of GOOGL share price based on the above assumptions. Make a recommendation based on GOOGL’s share price on 03/28/2024. (10 points)

3.   Quant Equity (40 points)

You are interested in evaluating the following big tech companies:

-    INTC

-    NVDA

-    AAPL

-    GOOGL

Download from Yahoo Finance monthly stock prices from 1/1/2011 to 12/31/2023 for these tickers and S&P 500 (^GSPC) index.

a.   Momentum (20 points)

Use the whole sample to compute a momentum strategy returns where you long the two highest momentum and short the two lowest momentum stocks. The portfolio returns are equal-weighted. Rebalance the positions every month. Compute the following:

i.   Mean return, volatility, Sharpe ratio (ignore interest rate) (10 points)

ii.   Regress the long-short returns on S&P 500 returns, and report alpha, beta, and state whether they are significant, and what that means. (10 points)

b.   Short-Term Reversal (20 points)

Use the whole sample to compute a short-term reversal strategy returns where you long the two lowest previous-month-return and short the two highest previous-month-return stocks. The portfolio returns are equal-weighted. Rebalance the positions every month. Compute the following:

i.   Mean return, volatility, Sharpe ratio (ignore interest rate) (10 points)

ii.   Regress the long-short returns on S&P 500 returns, and report alpha, beta, and state whether they are significant, and what that means. (10 points)

4.   Margin Requirements (10 points)

Suppose you are a hedge fund manager. You only have two positions:

-    Cash position that is worth $5 billion.

-    Short position that is worth $10 billion.

Your broker requires a 125% margin on your short position.

a.   How much extra cash should you post as margin other than the value of the short position? (5 points)

b.   On the next day, your short position moves against you by going up by 25%