More on risk and return

Objective Describe Robert Haugen’s experiments on the risk-return relationship in the stock market

Outline Experiment 1 Experiment 2 Experiment 3

EXPERIMENT 1: Historical standard deviation and realized returns for small and large stocks. Small stocks First quarter: Follow the rules below and construct a minimum variance portfolio over the trailing 24 months. At the end of the quarter record the realized portfolio return. Rules 1. No less than 0% more than 5% of the portfolio can be invested in any stock 2. No more than 20% of the portfolio can be invested in any one industry 3. No stock can have a weight higher than three times its % of the market's total value 4. turnover in the portfolio is constrained to 20% : Second quarter: Re-balance your portfolio and at the end of the quarter and record the realized return. Keep doing this each quarter for 60 years. Redo the above procedure, constructing this time a maximum variance portfolio.

EXPERIMENT 1: Historical standard deviation and realized returns for small and large stocks (cont’d). Large stocks Redo the above procedure for large stocks as well.

Observed relationship between historical minimum variance portfolios and average annual returns of American stocks ( ) Trend line

when accounting for stock size. Observed relationship between historical minimum variance portfolios and average annual returns of American stocks ( ) when accounting for stock size. Small stocks Large stocks

when accounting for stock size. Observed relationship between historical minimum variance portfolios and average annual returns of American stocks ( ) when accounting for stock size. Small stocks Large stocks Trend line

when accounting for stock size. Observed relationship between historical maximum variance portfolios and average annual returns of American stocks ( ) when accounting for stock size. Small stocks Large stocks Trend line

Comments an observed There is an observed direct relationships between risk and returns across all stocks. observed When splitting the stocks into large and small, the observed relationship becomes inverse.

EXPERIMENT 2: The relative performance of the minimum variance portfolio minimum variance portfolio Calculate the minimum variance portfolio just as in EXPERIMENT 1, without accounting for size. market index (S&P 500). Each quarter calculate the difference between the realized return of the portfolio and the realized return of the market index (S&P 500). Keep doing this for over 60 years. minimum variance portfoliomarket index In the end, calculate the cumulative difference of return between the minimum variance portfolio and the market index year by year.

Cumulative difference in returns between the minimum variance portfolio and the market index 0% 20% - 30% Since the 1970s, the minimum variance portfolio has outperformed the market index !

Comments In the 1920s... It was fashionable to invest in the stock market. expensive After several years of solid economic growth, investing in expensive stocks had become a fad. The crash market of 1929 ended the growth stocks craze.

Comments In the 1930s, 1940s, and 1950s... Graham and Dodd's Security Analysis was the bible of investing. The common wisdom said invest only in value stocks, that is, stocks with good current performance. Trying to predict growth in a reliable manner was considered impossible. Value stocks = good stocks. Growth stocks = speculative stocks. Tedious research had to be done in order to screen out overpriced stocks.

Comments In the 60s, 70s and 80s… Economists discovered that markets are efficient, hence its impossible to beat the market. Growth (expensive) stocks were not overpriced because their earnings were expected to grow long and strong into the future. Their volatility of return was obviously higher because they were considered riskier. CAPM and the market efficiency theory spawned hundreds of mutual and index funds.

Comments In the 1990s... Technology stocks become the object of desire. Dotcoms with no positive earnings on record sold at astronomical high prices.

EXPERIMENT 3: Historical performance of small and large stocks in relation to their market risk. Divide stocks into several portfolios from small to large. Calculate the market beta of each portfolio based on last year's data. At the end of the year, record the realized return for each portfolio Next year, re-group the stocks according to size, re-calculate the beta of each portfolio, and record end-of-year returns. Keep doing this for 50 years ( ).

Relationship between beta and portfolio return Trend line

Large stocks Small stocks Relationship between beta and portfolio return when accounting for size

Large stocks Small stocks Trend line

Discussion When ignoring size, there is a direct relationship between average beta and realized portfolio returns. When accounting for size, inside each size class the relationship becomes inverse. risk premiumliquidity premium. What the theory labels a risk premium appears to be a liquidity premium.

Concluding remarks: Is CAPM wrong? Not necessarily. expectedbeta required returns CAPM says there is a direct relationship between expected beta and required returns. observed beta realized returns What we see is an inverse relationship between observed beta and realized returns. CAPM could be right, but markets could be inefficient, that is, realizations do not equal expectations in the long run. However, we cannot observe expectations, and hence we cannot dissociate CAPM from market efficiency and tell which one is wrong.