Module 2: Portfolio Return, Risk, and Diversification

Question 1

What is portfolio theory?

Answer 1

Portfolio theory is a framework in finance for constructing and managing investment portfolios. Its key principles include:

1. Diversification: Spreading investments across different assets to reduce risk.
2. Risk-return tradeoff: The idea that higher potential returns generally come with higher risk.
3. Asset allocation: Distributing investments among various asset classes like stocks, bonds, and cash.
4. Efficient frontier: A set of optimal portfolios offering the highest expected return for a given level of risk.
5. Modern Portfolio Theory (MPT): Developed by Harry Markowitz in the 1950s, it provides a mathematical framework for portfolio selection.
6. Risk measurement: Using statistical measures like standard deviation to quantify portfolio risk.
   Correlation: Considering how different assets move in relation to each other to balance portfolio risk.

Question 2

How is speculation defined?

Answer 2

The assumption of considerable investment risk to obtain commensurate gain.

Question 3

How is considerable risk defined?

Answer 3

Risk is sufficient to affect the decision

Question 4

What is commensurate gain?

Answer 4

Positive risk premium, that is, an expected return greater than the risk-free alternative.

Question 5

What does it mean to gamble?

Answer 5

To bet or wager on an uncertain outcome.

Question 6

How do gambling and speculation differ?

Answer 6

In gambling - assumption of risk for enjoyment of the risk itself, whereas speculation is undertaken in spite of the risk involved because one perceives a favorable risk–return trade-off.

Question 7

What is meant by a fair game?

Answer 7

A risky investment with a risk premium of zero. no expected gain to compensate for the risk entailed.

Question 8

Would a risk averse individual reject gambles but entertain speculative investments?

Answer 8

Yes

Question 9

What types of investments do risk averse individuals take?

Answer 9

Risk-free or speculative. Not gambles or fair-game (or worse).

Question 10

What is the investor utility score for competing portfolio?

Answer 10

CFA Institute assigns a portfolio with expected return E(r) and variance of returns σ2 the following utility score:

U = E(r) - 1/2*Aσ^2
A is the index of an investors aversion - larger values with higher aversion.

Question 11

Is the utility score of risky portfolios a certainty equivalent rate of return?

Answer 11

Yes. The certainty equivalent is the rate that a risk-free investment would need to offer to provide the same utility as the risky portfolio.

Question 12

What are risk neutral investors?

Answer 12

A = 0

Judge risky ­prospects solely by their expected rates of return. Impose no penalty for risk, so a portfolio’s certainty equivalent rate is simply its expected rate of return.

Question 13

What are risk loving investors?

Answer 13

(for whom A < 0) is happy to engage in fair games and gambles; this investor adjusts the expected return upward to take into account the “fun” of confronting the
prospect’s risk

Always take fair game. Their upward adjustment of utility for risk gives the fair game a certainty equivalent that exceeds the alternative of the risk-free investment.

Question 14

How is the rate of return on the complete portfolio calculated?

Answer 14

r​ C​​ = yrP​​ + (1 − y )​​​​* rf​​​

y = proportion of risky asset

Question 15

How is the expected return on the complete portfolio calculated?

Answer 15

E(rC) = yE(rP) + (1 − y)rf = rf + y[E(rP) − rf]

y = proportion of risky asset

Question 16

Slope of capital allocation line

Answer 16

Equals the increase in the expected return of the complete portfolio per unit of additional standard deviation—in other words, incremental return per incremental risk.

S =
rise
____
run
=
E ( r​  P​​​ )
−
 ​ r​  f
_______
σ​  P

Question 17

What is the capital allocation line?

Answer 17

All the available risk–return combinations from the set of feasible expected return and standard deviation pairs of all portfolios resulting from different values of y

Question 18

How is the utility maximization determined for allocation to risky assets in a portfolio?

Answer 18

Optimal position in the risky asset is inversely proportional to the level of risk aversion and the level of risk (as measured by the variance) and directly proportional to the risk premium offered by the risky asset.

Max
y​ ​ U =
E ( r​  C​​ ) − ½ A σ^2  C
 ​ =
r​  f​​ + y [E ( r​  P​​ ) − r​  f​​ ] − ½ A y^2σ​^2  P

Question 19

What is the capital market line?

Answer 19

Capital allocation line provided by short-term T-bills and a broad index of common stocks. Represents a passive strategy.

Question 20

What is the top-down process of an investment decision?

Answer 20

(1) capital allocation between the risky portfolio and risk-free assets,
(2) asset allocation within the risky portfolio across broad
asset classes (e.g., U.S. stocks, international stocks, and long-term bonds)
(3) security selection of individual assets within each asset class.

Question 21

What are the benefits of asset diversification?

Answer 21

Diversification can reduce risk to arbitrarily low levels. The reason is that with all risk sources independent, the
exposure to any particular source of risk is reduced to a negligible level.

Question 22

What is the insurance principle?

Answer 22

Diversification when it writes many policies insuring against many independent sources of risk, each policy
being a small part of the company’s overall portfolio.

Question 23

What is market risk?

Answer 23

Risk that remains even after extensive diversification

Question 24

What is risk that can be eliminated by diversification?

Answer 24

Unique risk, firm-specific risk, nonsystematic risk, or diversifiable risk.

Question 25

How do we diversify risk?

Answer 25

By weighting their contribution in the portfolio.

rp = wDrD + wErE

E(rp) = wD E(rD) + wE E(rE)

σ​^2 = wd^2* σd​^2 + we^2* σe^2 + 2wdwe*CoV(rd, re)

Question 26

How is the covariance computed from a correlation coefficient (pde)?

Answer 26

Cov(rD, rE) = ρDE σDσE

σ​  =w​D​​σ​D​​ + w​E​σ​E​​

​​

Question 27

Why is it important that a hedge asset has a negative correlation with the other assets in a given portfolio?

Answer 27

Portfolio’s expected return is the weighted average of its component expected returns, whereas its standard deviation is less than the weighted average of the component standard deviations, portfolios of less than perfectly correlated assets always offer some degree of diversification benefit.

The lower the correlation, the greater the benefit.

Question 28

How is the portfolio standard deviation calculated?

Answer 28

σ​  =|w​D​​σ​D​​ - w​E​σ​E​​|

Question 29

What is the minimum-variance portfolio?

Answer 29

Has a standard deviation smaller than that of either of
the individual component assets

Question 30

What is the portfolio opportunity set?

Answer 30

Shows all combinations of port-folio expected return and standard deviation that can be constructed from the two
available assets.

Question 31

What is the objective function to find the weights of a portfolio that result in the highest slope of the CAL?

Answer 31

Sharpe ratio

sp = (E(rp) - rf)/σ​p

Question 32

How are the weights of the optimal risky portfolio calculated?

Answer 32

wd = (E(Rd)σe^2 - E(Re)Cover(Rd, Re))/(E(Rd)σe^2 - [E(Rd) + E(Re)]*Cov(Rd, Re))

we = 1 - wd

Question 33

Why does the minimum-variance frontier of risky assets?

Answer 33

The lowest possible variance that can be attained for a given portfolio expected return to help investor determine risk-return opportunities.

Question 34

What is the efficient frontier of risky assets?

Answer 34

Portion of the frontier that lies above the global
minimum-variance portfolio

Question 35

What is the separation property?

Answer 35

Tells us that the portfolio choice problem may be separated into two independent tasks

Question 36

How is portfolio variance calculated?

Answer 36

σ^2 = 1/n*σ^2 + ((n-1)/n) * cov

σ^2 = 1/n*σ^2 + ((n-1)/n) * pσ^2

Question 37

Why is time diversification a fallacy?

Answer 37

Underlying risk remains and cannot be mitigated.

Question 38

What is risk pooling?

Answer 38

Pooling together many sources of independent risk sources, is only part of the business model of the insurance industry

Question 39

What is risk sharing?

Answer 39

As more and more policies are pooled together, they are shared by ever-more investors, thus preventing any individual’s total risk from growing with the number of policies.

As more policies are added to the insured pool, each investor’s exposure to any single policy
shrinks. The law of averages does work—but you must make sure not to inadvertently scale up your bet as you “diversify” across many sources of risk