Class 10: Leverage

Question 1

What’s the formula of an equally weighted portfolio?

Answer 1

W becomes 1/_N because in an equally weighted portfolio all weights are equal. For example, if we had 3 stocks then N=3 so the weight would be 1/_N=⅓

Question 2

What happens to the risk if we hold a large/infinite number of stocks? Does it disappear?

Answer 2

NO! Risk does not ever disappear. There are two types of risk:

1. UNIQUE RISK -→ which becomes smaller as we diversify
2. SYSTEMATIC RISK -→ Does not become small, it can’t be diversifiable.

Diversification can eliminate some of the risk but not all, there is some risk that never goes away, in this case the risk is equal to the average covariance (market risk).

Question 3

Examples of low and high systematic risk?

Answer 3

Industries with

1. Low systematic risk: home staples such as food and utilities
2. High systematic risk: luxury goods and cars

Question 4

Real Estate Example Part 1

• Assume that the Seattle real estate market has an expected annual rate of return of 5% and a standard deviation of 8%. You buy a $1.5 million house in Queen Anne by putting down $300,000 in cash and borrowing the rest at an annual effective risk-free rate of 3.5%.

What is the first step to calculate the expected return and standard deviation of your portfolio?

Answer 4

The first step is to figure out the weights in your portfolio

Question 5

Real Estate Example Part 2

• Assume that the Seattle real estate market has an expected annual rate of return of 5% and a standard deviation of 8%. You buy a $1.5 million house in Queen Anne by putting down $300,000 in cash and borrowing the rest at an annual effective risk-free rate of 3.5%.

Steps 2 & 3: Calculate the expected return and standard deviation of your portfolio.

Answer 5

Step 2: Calculate the return on the portfolio

Step 3: Calculate the standard deviation of the portfolio, remember this is a risk free asset so use simplified formula

Question 6

What’s the formula for expected return portfolio of Coca Cola (KO) and a risk free asset? And what kind of graph is it?

Answer 6

I’s a straight line. Any combination of risk-free asset + risk stock (in this case Coca-Cola) lie along a straight line.

E[r_portfolio] =

Question 7

What is the most efficient portfolio combining risk with risk-free asset?

Answer 7

The Tangent portfolio, which is the portfolio with maximum return and lowest possible risk. I has the maximum slope and highest sharpe ratio.

Question 8

What’s the Sharpe Ratio? What’s the formula?

Answer 8

It’s the slope of the line joining the risk-free asset to a risky asset. It measures the trade-off between risk and return for a particular stock. Investors want higher return per unit of risk (steeper slope) so high Sharpe ratio.

Question 9

If the demand [All investors hold the optimal tangency portfolio] and the supply [all shares of all companies], then the tangency portfolio must be…

Answer 9

The market portfolio, it’s basically the S&P500

Question 10

What’s Beta?

Answer 10

Beta is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. It represents the asset’s sensitivity to the market portfolio.