week 7: portfolio Theory

Question 1

What are the two aims of modern portfolio theory?

Answer 1

MPT aims to create an optimal (or efficient) portfolio that could offer:

The highest return for a given amount of risk (𝜎_P)

The lowest risk for a given amount of return (𝐸(𝑟_P))

Question 2

what are the three generic parts of the investment decision process?

Answer 2

The Investment Decision Process consists of the following three generic parts:

1) Capital allocation between a risky portfolio and a risk-free asset (i.e., risky vs. risk-free)

2) Asset allocation across broad asset classes (within the risky category), such as Stocks, Bonds, etc.

3) Within each asset class, select individual assets/securities

Question 3

What is capital allocation?

Answer 3

A straightforward way to control portfolio risk is through the fraction of the portfolio invested in

Risk-free assets (e.g., T-bills)
Risky assets.

i.e., a choice among broad investment classes.

Question 4

What is the slope of the capital allocation line (CAL)?

Answer 4

the slope of he cpaital allocation line (CAL) is the excess return of the risky portfolio P per unit of risk (standard deviation).

Known as the reward-to-volatility or Sharpe ratio (S).

Question 5

Explain passive vs active investment strategy?

Answer 5

Passive Investment Strategy

• No security analysis; invests in index funds, ETFs, or mutual funds.
• Low information costs and management fees.
• Relies on the Capital Market Line (CML), which represents expected returns for portfolios combining a risk-free asset and the market portfolio.

Active Investment Strategy

• Aims to beat market returns through security selection, market timing, and portfolio optimization.
• Involves high information costs and management fees.
• Uses the Capital Allocation Line (CAL), based on an investor’s optimal risky portfolio.

Footnote:
CML assumes all investors hold the market portfolio and differs from the CAL, which reflects an individual investor’s mix of the risk-free asset and their chosen risky portfolio.

Question 6

What is the Capital market line (cml)?

Answer 6

The Capital Market Line (CML) is a specific Capital Allocation Line (CAL) formed using a risk-free asset (F) and a market portfolio (P) that mimics a broad market index (e.g., S&P 500).

The slope of the CML equals the Sharpe Ratio of the market portfolio, representing the best risk-return combinations available to investors under equilibrium.

Question 7

What does risk reduction depend on in a portfolio of two risky assets?

Answer 7

Risk reduction depends on the correlation coefficient ρ:

If ρ = +1.0, no risk reduction is possible.

If ρ = 0, σP may be less than the standard deviation of either component asset.

If ρ = -1.0, a riskless hedge is possible.

Question 8

What are the three key asset classes in portfolio construction?

Answer 8

the three key asset classes in portfolio construction are Stocks (E), Bonds (D), and T-bills (F)

Question 9

What does adding a risk-free asset (T-bills) to a portfolio allow us to do?

Answer 9

adding a risk-free asset (T-bills) to a portfolio allow us to determine optimal asset allocation across risky and risk-free investments.

Question 10

Why is understanding asset allocation with three asset classes important?

Answer 10

understanding asset allocation with three asset classes important Because it simplifies constructing optimal portfolios from many risky securities.

Question 11

What is the main question addressed when adding risk-free assets to a portfolio of stocks and bonds?

Answer 11

the main question addressed when adding risk-free assets to a portfolio of stocks and bonds is How much to allocate to each of the three: stocks (E), bonds (D), and T-bills (F)

Question 12

What are portfolios formed by mixing two risky assets typically composed of?

Answer 12

portfolios formed by mixing two risky assets typically composed of Stock funds (E) and bond funds (D).

Question 13

What is the objective in the optimal risky portfolio problem?

Answer 13

the objective in the optimal risky portfolio problem is to maximise the sharpe ratio which is the Reward-to-volatility ratio

Question 14

What constraint is applied in the optimal risky portfolio weight problem?

Answer 14

The sum of the weights must equal 1:

∑𝑤𝑖=1

Question 15

what are the steps for building a risky portfolio with two riksy assets and a risk free asset?

Answer 15

1. Specify the return characteristics of the securities (expected returns, variances, and covariances).
2. Establish the risky portfolio:
   A. Calculate the optimal risky portfolio P (using the equation in the last slide).
   B. Calculate the properties (expected returns and standard deviations) of Portfolio P using the weights determined in (a) and the equations in slide #25.
3. Allocate funds between the risky portfolio P and the risk-free assets (F).

A. Calculate the fractions of the complete portfolio allocated to P (fraction = y) and F (fraction = 1-y) using 𝒚^∗=(𝑬(𝒓_𝑷 )−𝒓_𝒇)/(𝑨𝝈_𝑷^𝟐 ).

B. Calculate the share of the complete portfolio invested in each asset and in F.

Question 16

Q: What summarizes the risk-return opportunities among risky assets?

Answer 16

A: The minimum-variance frontier.

Question 17

what are the steps of the The Markowitz Portfolio Selection Model?

Answer 17

Step #1 of the optimization is to determine the risk-return opportunities available to the investor.

Summarized by the minimum-variance frontier of risky assets.

Step #2 - the optimization now involves the risk-free assets.

We search for the capital allocation line (CAL) with the highest reward-to-volatility ratio (i.e., the steepest slope).

Step #3 - the investor chooses the appropriate mix between the optimal risky portfolio P and T-bills y= E(rp) - rf / A𝜎 𝑃^2

Question 18

Q: Does a portfolio manager create different risky portfolios for clients with different risk preferences?

Answer 18

A: No — the same optimal risky portfolio (P) is offered to all clients.

Question 19

Q: Where does risk aversion influence portfolio selection?

Answer 19

A: In choosing the desired point along the Capital Allocation Line (CAL) — i.e., how much to invest in the risky portfolio vs. the risk-free asset.

Question 20

Q: What is the separation property?

Answer 20

It’s the idea that portfolio choice can be split into two independent tasks:

Determining the optimal risky portfolio (technical task)

Choosing allocation between risky and risk-free assets (preference-based)

Question 21

What does the separation property imply about mutual fund offerings?

Answer 21

All investors could be satisfied with just two funds:

A money market fund (risk-free asset)

A fund holding the optimal risky portfolio (P)

Question 22

What are the benefits of the separation property for portfolio management?

Answer 22

Enables professional management to be efficient and low-cost by offering the same risky portfolio to all clients.

Question 23

Why might some investors still need customized portfolios despite the separation property?

Answer 23

Due to specific constraints like taxes, dividend-yield requirements, or other personal circumstances.