Lecture 2

Question 1

Please describe the bottom up approach when it comes to investing

Answer 1

Security Selection: produce the input list with the estimates of
assets’ expected returns and a covariance matrix by performing a security analysis.

Asset Allocation: select the composition of risky portfolio across broad asset classes (e.g. stocks, long-term bonds). Find the optimal risky portfolio (P), calculate its expected return and variance.

Capital Allocation: allocate funds between risky portfolio and risk-free asset (e.g. Treasury bills) based on the degree of risk aversion. Find the optimal complete portfolio (C), calculate its expected return and variance.

Question 2

Please list the formulas for return, expected return and variance for a portfolio with two assets

Answer 2

Question 3

What is the minimum variance portfolio and what is the formula?

Answer 3

The minimum variance portfolio can be defined as the portfolio of risky assets with the lowest possible variance

Question 4

Assuming the portfolio weights are constant, please describe the impact of ρ1,2 = 1, -1 < ρ1,2 < 1 and ρ1,2 = -1 on variance (risk)

Answer 4

When correlation (ρ1,2) = 1. We see that the two assets are perfectly correlated. As such variance of the portfolio will be σP = ω1σ1 + ω2σ2

For -1 < ρ1,2 < 1, the investor will gain some benefits of diversification

For (ρ1,2) = - 1, the assets are perfectly negatively correlated. Assets with negative correlation are known as a hedges. σP = |ω1σ1 − ω2σ2|

Question 5

What is asset allocation and what is the key idea behind it?

Answer 5

Asset allocation pertains to combining the risky portfolio constructed of two assets with a risk free asset.

The key idea is to maximize the risk premium per unit of risk

Question 6

Please provide Return, Expected Return and Variance of the complete portfolio:

Answer 6

*y essentially represents weight

Question 7

What do you obtain when you combine E(rc) and σc^2. Please provide the formula

Answer 7

Capital Allocation Line (CAL), which is all the risk-return combinations for various weights.

Question 8

What does the Sharpe ratio describe. Please also provide formula

Answer 8

The Sharpe ratio, also known as the reward-to-volatility ratio describes the increase in return per unit of extra risk

Question 9

Please explain why y<1 is lending and y>1 is borrowing

Answer 9

When investor borrows in the risk-free rate (t-bills, etc.) i.e. borrows, his position in risky asset becomes levered. The expected return as well as risk are escalated,
but reward-to-volatility ratio remains the same.

Question 10

How do we find the optimal risky portfolio?

Answer 10

We find the weights for the portfolio that maximize the sharpe ratio:

Question 11

Please describe how the optimal risky portfolio differs from capial allocation

Answer 11

The optimal risky portfolio is derived irrespective of the investor’s risk preferences. However, capital allocation (how much is put in risk-free assets versus in the risky portfolio) differs depending on the investor’s risk preference

Question 12

Please state the quadratic risk function and the meanings of ‘A’ in it

Answer 12

U = E(rp) − 0.5Aσ^2p

A represents the degree of risk aversion possessed by the investor.
A > 0: risk averse
A = 0: risk neutral
A < 0: risk lover

Question 13

Please describe what a utility score is

Answer 13

The utility score can be described as the certainty equivalent rate (CER) of return score. Thus, it is the return a risk-free investment has to provide to provide the same utility as a risky portfolio.

The portfolio is desriable when the CER exceeds the return on the risk-free asset

Question 14

What are indifference curves? What is on the X and Y axes?

Answer 14

On the X-axis is risk and on y-axis is return.

The indefference curve represents combinations of risk and return that yield the same level of utility. Therefore, portfolios are only attractive if they lie on or above the investor’s indifference curve.

Risk averse investors have steeper curves.

Question 15

How would you compute the optimal complete portfolio, C?

Answer 15

Question 16

Please describe each element in this graph

Answer 16

CAL(P): A straight line representing the combinations of risk-free asset and the risky portfolio. It’s slope is the Sharpe ratio of the risky portfolio

P: Optimal risky portfolio (entirely invested in the risky portfolio)
C: Optimal complete portfolio (where the indifference curve is tangent to the CAL - some funds invested in the risk-free asset)
E: A set of risky assets on the efficient frontier

Question 17

Please summarize the security selection, asset allocation, capital allocation process

Answer 17

1. Security Selection: specify the return characteristics of all securities (expected returns, variances, covariances). Important: securities themselves are ideally already diversified portfolios. Diversification within each asset class to be invested leads to a significant risk reduction.
2. Asset Allocation: find the optimal risky portfolio (P) and calculate its expected return and variance
3. Capital Allocation: allocate funds between the optimal risky portfolio (P) and risk-free asset based on the degree of risk aversion. Find the optimal complete portfolio (C), calculate its expected return and variance.

Question 18

What is the seperation principle?

Answer 18

Given (1) the identical investable universe of risky assets and riskfree asset, (2) the same set of constraints and (3) identical estimates of asset expected returns, variances, etc., the whole process of portfolio construction can be split into two independent tasks. First, the optimal risky portfolio P is the same for all clients, regardless of their risk aversion, since all the investors will have exactly the same efficient frontiers and CAL. However, second, capital allocation between
risky and risk-free assets will depend on personal preference i.e. risk
aversion.