CAIA L2 - 1.6 - An Introduction To Portfolio Rebalancing Strategies

Question 1

Define

Payoff diagram (Portfolio Value X Equity Value) of
Buy-and-Hold (BH)
Constant Mix (CM) and
Constant Proportion Portfolio Insurance (CPPI)

1.6 - An Introduction to Portfolio Rebalancing Strategies

Answer 1

BH - linear
CM - concave
CPPI - convex

1.6 - An Introduction to Portfolio Rebalancing Strategies

Question 2

Formula

Target equities investment
of the
CPPI re-balance

1.6 - An Introduction to Portfolio Rebalancing Strategies

Answer 2

Target equities investment = M x (Portfolio Value - Floor Value)

M = multiplier (constant proportion, higher than 1)

1.6 - An Introduction to Portfolio Rebalancing Strategies

Question 3

List

2 unique risks
of pursuing CPPI

1.6 - An Introduction to Portfolio Rebalancing Strategies

Answer 3

1. Gap risk - risk of violating the floor (not time enough to re-balance)
2. Absorption risk - risk of missing a rising market after equity exposure is reduced to zero

1.6 - An Introduction to Portfolio Rebalancing Strategies

Question 4

Formula

Return of Illiquid asset
(in dinamic rebalancing strategy,
using a liquid financial instrument, like future)

1.6 - An Introduction to Portfolio Rebalancing Strategies

Answer 4

return on illiquid asset ‘t’ = R’f’ + α + (β × Futures’t’ ) + ε

R’f’ = risk-free rate of return

α = alpha of the illiquid asset portfolio

β = beta of the illiquid asset relative to futures

ε = tracking error

1.6 - An Introduction to Portfolio Rebalancing Strategies

Question 5

Formula

Weight of Futures in a
dynamic rebalancing using futures

1.6 - An Introduction to Portfolio Rebalancing Strategies

Answer 5

F’t’ =[ (α / R’F,t’) + β ] * ( k’t’ - w’t’ )

F’t’ = weight of futures position (i.e., the proxy)

R’F,t’ = expected return on the futures

k’t’ = optimal weight of risky asset

w’t’ = current weight of the illiquid risky asset

Example: CPPI for Illiquid Asset
A portfolio is currently comprised of $1,000 in real estate and $1,000 in cash. The portfolio manager wants to implement a CPPI strategy with M = 2 and floor = $400. The real estate portfolio has a beta of 1.10 relative to the futures on a REIT index. The index expected return is 6% while the risk-free rate is 2.5%. The manager’s historical alpha (relative to the index) is 1%. Calculate the allocation to futures to implement the CPPI strategy.
Answer:
The current weight of real estate in the portfolio = wt = 1,000 / 2,000 = 50%
CPPI allocation to real estate = M × (V0 – F) = 2 × (2,000 – 400) = $3,200
Optimal weight of risky asset = kt = 3,200 / 2,000 = 160%
Ft= ( (α/RF,t)+β ) (kt−wt)
= ( (0.01/0.06)+1.10 ) (1.60−0.50)
= 1.39

1.6 - An Introduction to Portfolio Rebalancing Strategies