Long Maths Qs Flashcards
Portfolio Variance
Markowitz formula
Cov (ra,rb) = Corr(a,b) x SDa x SDb
var = SD squared
CPPI
Constant portfolio protection insurance
- dynamic allocation between risky and safe assets
- guarantees preservation of capital in market falls through the risk free asset
CPPI Steps
- Set floor (min value to be protected)
- Calc cushion (difference between current value and floor)
- Calc multiplier (1/x, x = worse case estimated loss in period)
- Multiplier x cushion = goes into risky asset
- Review + rebal (whole process from step 1)
FLOOR CUSHION MULTIPLIER
RISKY SAFE
Pros and cons of CPPI
PROS
- preserves capital while still allowing you to make gain through risky asset
- no leverage so reduced risk
- doesnt forgo gains by being only in safe asst
- useful when future lump sum must be presered - will always protect floor as long as loss assumption is correct
CONS
- in bull run could end up with all of portfolio in risky
- trading costs can be v expensive (annual turnover @ rebal may be serious)
- cushion is rebuilt v slowly after max expected loss
- increasingly removes upside potential
- may miss market rises that follow large drops
- OW risk assets until there is a loss event
Pros and cons of trad LTAA
PROS
- inexpensive trading since relatively passive
- appropriate where investor happy to bear LT risks w/out liabilities
- designed to see through ST and deliver on future value
- good for large investors with good capacity for loss
- doesnt req intensive management
CONS
- not adaptive to changing conditions
- rebalancing is arbitrary
- can be an element of luck if a liability is met
- focus on meeting long term objective on average
RISK PARITY
Approach based on equal weighting of risk - constructs portfolio so that the allocations across assets have the same contributions to risk
- e.g. a 60/40 portfolio has very unequal contributions to risk (maybe 90% risk in equities)
Assumes no correlation between assets
Tends to be based on MPT - with risk/return assessed as single
Returns from risk parity portfolio (with resultant high bond exposure) can be v low
= can compensate for this with leverage
RISK PARITY PORTFOLIO Q
eq SD = 10%
Bond SD = 5%
- Work out eq and bond weighting such that cont. to risk is equal
Eq = 5/15 = 33%
Bonds = 10/15 = 66%
- Sense check with Markowitz formula (1st two bracketed items should be equal)
Riskier asset should have lower weighting
Assumes no correlation between assets so 3rd bac should be 0
- Work out EOY values based on performance and reweight to risk parity weights
PROS and CONS of risk parity portfolio
PROS
-Risk targets put focus on portfolio diversification/risk control
- should make performance smoother and more stable
- dont need estimate of expected returns to implement - forecasting returns is riskier than forecasting risk
CONS
- assumes risk is well represented by vol which is proven flawed by VaR methodologies
- several asset classes also have negative skew (non normal risk distros)
- incorporates no views on future returns - included assets may have 0/-ve risk premiums
-
RISK PARITY WITH LEVERAGE
Lever up risk parity portfolio such that it’s risk = total risk for SAA portfolio
1.Calc SD for SAA and for RP portfolios using Markowitz
- Leverage required = SD SAA/ SD RP portfolio
e.g. 6/3 so 2x levered - Apply leverage to total and work out weightings
- Apply perf to each year, deducting interest cost/borrowing and relevering each time @ rate (2x in this case)
PROS AND CONS OF RISK PARITY WITH LEVERAGE
PROS
- without leverage, risk parity can derisk too much so leverage counterbalances lost returns from holding high levels of low risk assets
- close to maximum sharpe ratio with leverage
- equity like returns w/out equity like risk with gearing
-Risk targets put focus on portfolio diversification/risk control whcih should make performance smoother
- dont need estimate of expected returns to implement - forecasting returns is riskier than forecasting risk
-leverage counterbalances lost returns due to holding more low risk assets
CONS
- client must be willing to undertake leverage
- unexpected inflation can make bond returns suddenly negative (high weighting)
- assumes risk is well represented by vol which is proven flawed by VaR methodologies
- several asset classes also have negative skew (non normal risk distros)
- incorporates no views on future returns - included assets may have 0/-ve risk premiums
- leverage may become expensive in high rate environment
- tax repercussions from high weighting to FI
ASSET LIABILITY MATCHING vs CPPI
Similar to CPPI - but difference since you retain a certain amount in protection portfolio to cover liability - rest goes into performance and is geared up
- with CPPI you dont retain the whole liability amount in the safer assets
CPPI = set floor, calc cushion, cushion x multiplier goes into risky
ALM = set safe/protection, calc multiplier and rest into risky
ALM = one where you set aside interest @ beginning
ASSET LIABILITY MATCHING
900k portfolio
600k liability
50% max loss
2% interest cost
- £ of liability = goes straight into protection portfolio
- Calc cushion and multiplier
Cushion = portfolio value - liability (300k)
Multiplier = 1/max loss (2x) - Cushion x multiplier = into risky
= 600k
so you are borrowing 300k - Calc interest at set aside
2% on 300k = 6k. 6k goes into safe - so gear up 294k 2x - Invest 2x 294k in risky (588k)
so even in max loss event you can still pay back 294k + interest in safe (INTEREST COST IS NOT 6K - IS IT 2% OF 294)
PROS AND CONS OF ALM
PROS
- good for investors with high risk tolerance but low capacity for loss
- leverage may allow u to achieve disproportionately high return for value of net assets
- low trading costs as no rebalancing
- no need to rebalance or move capital between two portfolios
- leverage = controlled risk taking- not endangering capital that must be protected
CONS
- costs associated with hedging instruments (e..g hedging rates on debt)
- leverage may be expensive if rates are high
- investor must be willing and able to undertake leverage
- focus on liabilities may hinder investment choices
-a lot hinges on accuracy of max drawdown fig
