The Four Lessons I Hope you Get out of 410 Final Review The Four Lessons I Hope you Get out of 410

Lesson #1 There are two sides to the investment decision: 1) Pick stocks that will maximize expected return 2) Pick stocks that will minimize risk Going with passive index funds does not have to be boring! If you want high expected returns, don’t dabble in penny stocks – lever up on the market. Doing so will get you high expected returns for much less risk.

The CAL Penny Stocks Market

Lesson #2 Math and statistics can be very helpful tools to help you make finance decisions. Help estimate the probability of extreme events 5% VAR Guide us in making the best use of past data.

PDF PDF: a function that describes the possibility of every possible outcome. If we know the PDF function, we know the probability of every possible outcome. Using the PDF we can compute true parameters Mean, variance, covariance, correlation These may help us make better decisions

Estimation We rarely know the exact PDF Instead we observe random samples of outcomes. These outcomes, and their frequency, allow us to estimate parameters. These estimated parameters, though imperfect, may help us make better decisions.

Example I Reasonable Definition: A skilled fund manager is one who has greater than a 50% chance of earning positive alpha. Question: Does a given fund manager have skill? For any given year there are two possible outcomes: A fund manager earns positive alpha Probability = p A fund manager earns zero or negative alpha Probability = (1-p)

Example I We don’t know the true value if p Our best recourse is to estimate p. Observe alpha each year for 10 years. Suppose he earns positive alpha in 6 of these 10 years. OK – we’re done, right? Invest with this fund! Hold on: even if the fund manager has no skill, there is some chance that he just got lucky. How many +alpha years does the poor chap have to earn to convince you he has skill?

Example I We don’t want to be bamboozled into giving our money to an unskilled manager. We want to set the bar so high that an unskilled manager would have less than a 5% chance of attaining the bar. The decision on “5%” is subjective If p=0.50 then There is a 5.4% chance of +alpha in 7 or more years There is 1.07% chance of +alpha in 8 or more years (You don’t need to know how I got these.)

Example I Null hypothesis: p=0.50 Bar: 8 or more years of positive alpha out of 10 T1 error: getting bamboozled: conclude unskilled manager has skill Prob(T1 error): 1.07%

Hypothesis Testing Let q = some true parameter Let = an estimate of this parameter Let q0= the null hypothesis Let se = standard error for Question: Does How far away does have to be from q0 for us to conclude that We want to specify our decision rule such that we only have a 5% chance of concluding that when in reality

Hypothesis Testing Null Hypothesis: T1 error: rejecting the null when it is true. If , then by laws of statistics, for any parameter estimated for any continuous PDF, we have only a 2.5% chance of getting If we make the above inequalities our rejection bounds, we have a 5% chance of making a T1 error. Standard error for

T-statistics Note that if We call Provided that the t-stat> 1.96 or t-stat<- 1.96 we reject the null.

Example I Returns: 0.05, 0.20, -0.10 Test the null hypothesis that

Lesson #3 The tangency portfolio should be close to the value-weighted market portfolio. Falls out from the assumptions of the CAPM. Passive strategies using value-weighted market ETFs can make a lot of sense.

Positive Alpha Strategies The tangency portfolio is probably not exactly equal to the value-weighted market portfolio. Evidence: value and momentum strategies earn positive alpha Persistent non-zero alpha is probably not evidence that value-and momentum strategies are mispriced, but rather (among other things) that rm is not the tangency portfolio.

Lesson #4 Beating the market – earning positive alpha – can still be very difficult. Fund managers have a hard time beating the market after fees, transactions costs, and cash drag Alphas of actively managed funds:

Efficient Markets However, in an “efficient” market, there will be rewards to doing research. Research Conducted SO who is it that is getting the rewards? Rewards for Research Market Efficiency