Stocks
Kevin Crotty
BUSI 448: Investments
Where are we?
Last time:
- Returns of portfolios
- Portfolio expected return
- Portfolio standard deviation
Today:
- Equity markets
Fundamental Asset Classes
Equity markets
Fixed income markets
Today, we’ll focus on some empirical facts about the stock market.
Some empirical facts for today
- Over long horizons, average returns in the US stock market have exceeded those of bonds.
- Stock returns are risky; that is, volatile.
- Stock return distributions are fat-tailed and negatively skewed.
- Past aggregate returns do not predict future aggregate returns.
- Volatility is time-varying and persistent.
Stock Market Indices
- S&P Indices
- 500, Midcap 400, Smallcap 600
- value-weighted index
- Dow Jones
- price-weighted index
- Russell
- 1000 + 2000 \(\rightarrow\) 3000
- MSCI int’l indices
- FTSE, DAX, Hang Seng, etc.
Annual Returns
Time-series
Distribution
Compounded return
value of $1 investment with dividends reinvested
Compounded returns on log scale: motivation
- Let’s look at accumulations from two hypothetical stocks.
- stock 1: 10% per year
- stock 1: 2% per year until 2000 and 10% afterwards
- It will appear that stock 2 did nothing before 2000 and earned a lot less than stock 1 even after 2000.
Plot of the Example
Log (base 10) of accumulation
Map \(y\) tick labels to dollars
Compounded market returns on log scale
value of $1 investment with dividends reinvested
Empirical record
Does last year’s return predict this year’s?
- How would we test this?
- Autocorrelation is the correlation of a time series with its own lagged values.
- Autocorrelation at lag 1 tells us whether the current value predicts the next one. \[ r_t = a + \rho \cdot r_{t-1} + \varepsilon_t \]
- What should be true of \(\rho\)?
Does last year’s return predict this year’s?
Monthly Returns
Time-series
Distribution
Empirical vs. normal distribution
Does last month’s return predict this month’s?
Autocorrelations
- For monthly data, autocorrelation might be high at lag 12 (seasonality).
Daily Returns
Daily market returns
Empirical vs. normal distribution
Normal distribution has same mean and std dev as actual.
x-axis range is minimum to maximum return.