WEEK 2 - Capital Allocation and Optimal Complete Portfolio

Question 1

What is the only difference in people’s choice of risky portfolios?

Answer 1

The portfolio of risky assets same to everyone, only difference here is attitude to risk

Question 2

What is the importance in diversification?

Answer 2

YOU KNOW THIS

Question 3

How do you calculate Weight of Assets in Portfolio?

Answer 3

wi = Value of Investment i / Total Value of Portfolio

Question 4

How do you calculate Expected Return of portfolio?

Answer 4

E (rp) = Sum of Wi x E (ri)

Wi = Weight of investment I 
E(ri) = Expected return of Investment i

Question 5

How do you calculate VAR of portfolio?

Answer 5

Sum of {(rp - E (rp) to the power of 2)}

Erp = Expected return on portfolio

EXAMPLE IN NOTES

Question 6

How do you calculate ST DEV of a 2 asset portfolio?

Answer 6

δ2P = Wa 2 x δ2a + Wb 2 x δ2b + 2WaWb COV(A,B)

JUST SQUARE ROOT AFTER

E(r) = WaRa + WbRb

Where 2 is the power of 2
δ2a = VAR of asset A

Question 7

What are the 2 requirements to Portfolio Construction?

Answer 7

1. Select Composition of risky portfolio
2. Decide how much to invest in it and rest in risk free investments (This part called Capital Allocation to Risky Assets)

All complete portfolios consist of Risky and risk free assets

Question 8

What can we use as a risk free asset?

Answer 8

No such thing as a truly risk free asset

-> In practise money market funds can be viewed as approx risk free: Tresury Bills,Repos

Question 9

How do we calculate the expected return of a complete portfolio (including risk free and risky assets)? EXAMPLE IN NOTES

Answer 9

E(rc) -rf = w (E(rp) -rf)

So,
E (rc) = rf + w(E(rp) - rf)

Where:
c = Total Portfolio

Question 10

What is the risk premium for C?

Answer 10

E (rc) - rf

Question 11

What is the risk premium?

Answer 11

Min amount of expected return on a risky asset must exceed risk free asset, to induce investor to hold on to risky portfolio

Question 12

How do we calculate the volatility in a complete portfolio? EXAMPLE IN NOTES

Answer 12

VAR = δ2c = w2δ2p
ST DEV. = Wδp

Where 2 is to the power of

Question 13

What is the capital allocation line?

Answer 13

Line showing combination of all distributions between risky and risk free assets

Question 14

How do we calculate the capital allocation line?

Answer 14

Using δc = wδp, expected return on a complete portfolio can be rewritten as a capital allocation line,

E(rc) = rf + δc/δp E (rp - rf)

Question 15

What is the slope of the CAL?

Answer 15

E (rp) - rf / δp

Question 16

What happen to the CAL if portfolio C’s weight is:

a. 0
b. 1
c. 1.5 etc.
d. A broad market index

Answer 16

When Portfolio C’s weight is at:

a. 0 -> Means all investment is in risk free asset
b. 1 -> Means all investment is in risky portfolio
c. 1.5 and greater -> Means the investor has borrowed to invest more
d. If portfolio C is broad mkt index like S&P500 then CAL is the market index line (Where the allocation line reps the allocation of the market)

SEE GRAPH IN NOTES

Question 17

What happens to the expected return in the CAL when:

a. VAR = 0 (δ=0)
b. VAR = VAR of Portfolio (δ = δp)

Answer 17

When:

a. VAR = O, the expected return is equal to the risk free rate
b. VAR = VAR of portfolio, the expected return is rf + E(rp - rf)

Question 18

What is the Sharpe ratio?

Answer 18

Its the slope of the CAL, representing risk/reward trade off -> For more risk how much do we get compensated.

Question 19

How do you calculate the Sharpe ratio?

Answer 19

Sp = E (rp) - rf / δp

ST DEV OF P = δp

Question 20

Why is/What happens as a result of the CAL being kinked at portfolio P?

Answer 20

Kinked since borrowing rate > lending rate

Mean if W = 2, the cost of borrowing much higher than W= 1.5

SEE GRAPH IN NOTES

Question 21

When is a Portfolio attractive to a risk averse investor?

Answer 21

Portfolio more attractive when risk down and E(r) up

Question 22

How do you calculate the Utility Function?

Answer 22

U = E(r) - 1/2 Aδ to the power of 2

Where:
A = Level of risk aversion = Higher A more risk averse
δ2 = VAR

Question 23

How do you tell if an investor is risk neutral, risk loving, risk averse?

Answer 23

If
the asset is Risk free U = Risk free rate (we see risk averse here)
A= 0, U depend only on E(r): Risk Neutral
A<0: Risk lover

For the portfolio (u) -> Is certainty equivalent
-> Risk free return give same utility as risky investment

Question 24

How is risk aversion represented in the optimal complete portfolio?

Answer 24

SEE GRAPH IN NOTES

Question 25

How can we find out what portfolio an investor should pick to maximise utility?

Answer 25

MAX U = rf + w(E(rp) - rf) - 1/2 A w2δ2p

two = power of 2
Investors will choose proportion w that maximises utility:

W* = e(rp)-rf / Aδ2p