Lab for Lecture 17: Review Session
1 Problem 1: Factor Model and Cost of Equity for NVDA
1.1 Data
Use the stock_returns_mag7.xlsx dataset to obtain monthly returns on NVIDIA (NVDA), and the fama_french_3_factors.xlsx dataset to obtain the market excess return (Mkt-RF), the SMB and HML factors, and the risk-free rate (RF).
From stock_returns_mag7.xlsx:
| Column Name | Data |
|---|---|
| Date | Date at monthly frequency |
| NVDA | Monthly return on NVIDIA |
From fama_french_3_factors.xlsx:
| Column Name | Data |
|---|---|
| Date | Date at monthly frequency |
| Mkt-RF | Monthly excess return on the market portfolio (market return minus risk-free rate) |
| SMB | Monthly return on the Small Minus Big factor |
| HML | Monthly return on the High Minus Low factor |
| RF | Monthly risk-free rate (1-month T-bill rate) |
1.2 Analysis
Using this data, and the Fama-French Three Factor Model, answer the following questions:
- What are the alpha and market beta of NVDA?
- Is NVDA underpriced or overpriced at the 1% significance level?
- What percentage of NVDA’s total variance is diversifiable?
- What is NVDA’s idiosyncratic variance?
- What is the annualized cost of equity for NVDA? Use the full sample of the Fama-French data (from 1926 onwards) to estimate the risk premia for each factor. Use the last available risk-free rate in the dataset as your risk-free rate.
- Assuming that NVDA’s after-tax cost of debt is 5%, and its leverage ratio is 20%, what is the annualized weighted average cost of capital (WACC) of NVDA?
2 Problem 2: Bond Pricing, Returns, and Risk
2.1 Setup
Assume today is 2020-01-01. Bond A has the following characteristics:
| Feature | Value |
|---|---|
| Maturity | Exactly 30 years from today (2050-01-01) |
| Quoted (flat) price today | 100 |
| Coupon rate | 6% |
| Coupon frequency | Semiannual |
| Par value | $1,000 |
| Day-count convention | Actual/365 |
2.2 Questions
- What is the yield to maturity (YTM) of the bond today?
- If its YTM does not change, what will be the quoted (flat) price of the bond on 2021-01-01?
- If its YTM does not change, what will be the invoice (dirty) price of the bond on 2021-03-01?
- Assume you buy the bond on 2021-01-01, can reinvest all the coupons at a 4% interest rate, and you hold the bond until maturity. What will be your annualized (APR) return from this investment?
- What is the modified duration of the bond, as of 2021-01-01?
- As of 2021-01-01 assume the bond’s YTM is still 6%. Use the bond’s modified duration to estimate the percentage change in the bond’s value if its YTM decreases by 0.1% that day.