CAIA L2 - 5.4 - Hedging, Rebalancing, and Monitoring Flashcards
Formula
Desired beta exposure βnew
as a function of adding futures exposure
5.4 - Hedging, Rebalancing, and Monitoring
β’new’ = β’p’+ (F/P) β’futures’
β’new’ = beta desired (target beta)
β’p’ = beta of a portfolio
F = futures size (notional)
P = portfolio size
5.4 - Hedging, Rebalancing, and Monitoring
Define
Portable alpha
5.4 - Hedging, Rebalancing, and Monitoring
Strategy to pursue alpha from a
benchmark other than the one used for beta management.
5.4 - Hedging, Rebalancing, and Monitoring
Formula
Put-Call Parity
5.4 - Hedging, Rebalancing, and Monitoring
+stock + put – call = +bond
all options are
* European options
* identical strike prices
* identical expiration dates
5.4 - Hedging, Rebalancing, and Monitoring
List
Option Sensitivities of long
* Stock (+S)
* Put (+P)
* Call (+C)
* S+P-C
(Delta δ, Gamma γ, Vega ν)
5.4 - Hedging, Rebalancing, and Monitoring
/////////+Stock //+Put//+Call//+Stock +Put –Call
Delta// 1 //δ – 1//δ//0
Gamma//0//γ//γ//0
Vega//0// ν//ν//0
5.4 - Hedging, Rebalancing, and Monitoring
Define
the slack variable
that traders use to optimize output
(trading with options)
5.4 - Hedging, Rebalancing, and Monitoring
the underlying asset as a slack variable that hedges the option trade against market movements, but it is not a source of alpha, gamma, or vega.
5.4 - Hedging, Rebalancing, and Monitoring
Define
traders position
depending on views of implied
vs expected (relized) volatility
5.4 - Hedging, Rebalancing, and Monitoring
Traders use options as a bet on volatility
Net long options : estimated implied volatility < expected (relized) volatility
Net short options estimated implied volatility > expected (relized) volatility
5.4 - Hedging, Rebalancing, and Monitoring
Formula
Delta hedge
+
3 observations
for risk managers
considering delta hedging
5.4 - Hedging, Rebalancing, and Monitoring
ΔHedge = Δc / ΔS
Value changes according to path, price movements
1. Delta hedging is not a directional bet. When options are properly priced, a delta-hedged strategy should produce a payoff of $0. If an investor is convinced that a stock is undervalued, then they would be better off taking a long position in the call option, in the stock, or in both.
Obs: In real markets, delta hedge payoff <> 0
2. Delta hedging is partly a bet on volatility. Delta-hedged investors are not making a directional bet or a play on the ultimate price level of the underlying security. They are betting that the market has misestimated the volatility on the underlying security that flows through to the pricing of the option. If an option is mispriced, then an arbitrage profit is possible if the analyst is correct in their estimation of the mispricing.
3. Efficiently priced stocks produce trading strategies with an NPV of zero. If stock prices are informationally efficient, then the expected payoff from a delta-hedged strategy should be zero. Some commentaries suggest that expected profits from delta hedging are the result of stock price movements. In reality, this strategy is based on the belief that a derivative is mispriced relative to the price of an underlying security.
5.4 - Hedging, Rebalancing, and Monitoring
Formula
3 key observations
on rebalancing
delta-neutral strategies
5.4 - Hedging, Rebalancing, and Monitoring
There are three key observations on rebalancing delta-neutral strategies:
- Infrequent rehedging is a bet on positive autocorrelation. Without rebalancing, a delta-hedged strategy will benefit from a directional price movement. If a stock’s price movement is directional, then a long gamma portfolio will benefit from infrequent rebalancing because the call option’s gamma will generate large gains (small loses) in an upward (downward) trending market. However, if a market is mean reverting, then the stock will return to its original price and the option will lose value due to theta. Thus, infrequent rebalancing is a bet on a directional (i.e., positive autocorrelation) outcome.
- Frequent rehedging is a bet on negative autocorrelation. When the underlying asset’s price follows a mean-reverting trend, more frequent rebalancing is beneficial. However, the rebalancing benefits need to be weighed against the increased transaction costs. Rebalancing after 1% directional moves will be more profitable than rebalancing after 2% moves, and it will be far less costly than rebalancing after 0.10% directional moves.
- Rehedging is more effective for short-dated options that are near the money. The effectiveness of a rebalancing program depends on the timing of volatility with respect to an option’s tenure and moneyness. Long-dated options have modest gamma, which reduces the profitability or rehedging. Gamma is also reduced when options are deeply in the money (i.e., delta near one) or deeply out of the money (i.e., delta near zero).
5.4 - Hedging, Rebalancing, and Monitoring
Define
Rebalancing (rehedging)
&
payoff / risk profile for:
* random walk market
* trending market
* mean reverting market
5.4 - Hedging, Rebalancing, and Monitoring
* random walk - rebalancing does not change the expected payoffs, but it does alter the risk profile.
* trending - rebalancing will lower the expected payoff while at the same time controlling risk.
* mean reverting - rebalancing will enhance expected payoffs while altering the risk profile.
Rebalancing in any environment is useful for reducing volatility and encouraging a focus on arithmetic returns
5.4 - Hedging, Rebalancing, and Monitoring
Formula
compounded return
f(arithmetic return, variance)
- all data per period
5.4 - Hedging, Rebalancing, and Monitoring
R’c’ ≈ R − 0.5 x σ^2
R’c’ = per-period compounded return
R = per-period arithmetic return
σ= per-period variance
Example
An investment analyst seeks to analyze the impact of portfolio rebalancing in a situation where asset prices have not displayed any form of mean reversion. The analyst observes that while ending values remain unchanged, the volatility is altered. Given the portfolio’s monthly arithmetic return and monthly standard deviation are 10% and 15% respectively, the monthly compounded return is closest to:
R’c’ ≈ 0.10 – 0.5 × 0.15^2
R’c’ ≈ 8.88%
5.4 - Hedging, Rebalancing, and Monitoring
Define
Diversification return
and
List scenarios that
Assets will benefit from rebalacing
5.4 - Hedging, Rebalancing, and Monitoring
Diversification return =
rebalancing’s extra geometric return
‘—
Assets will benefit from rebalancing under two scenarios:
1. Returns are highly volatile, and correlations are low with other assets.
2. Returns display mean-reversion tendencies.
Commodities meet both criteria. Example: energy, because it’s high prices lower demand and hinder business cycle
5.4 - Hedging, Rebalancing, and Monitoring
Define
Monitoring
5.4 - Hedging, Rebalancing, and Monitoring
ongoing process of
* gathering ,
* reviewing , and
* analyzing information
vital to the success of an investment strategy
5.4 - Hedging, Rebalancing, and Monitoring
List
two forms of activism
that occur between the general partner (GP)
and the limited partners (LPs)
in private equity fund governance
+
three forms of activism
that occur between the general partner (GP)
and the limited partners (LPs)
outside private equity fund governance
5.4 - Hedging, Rebalancing, and Monitoring
Dica: quantidade de letras:
* in =2 out =3
* in = 2 = ee ee (f ee ; agr ee ment)
Inside governance
1. Renegotiation of management fees. If a GP is not delivering on promised returns, especially toward the end of a strategy’s life cycle, then LPs may attempt to renegotiate management fees. An alternative is to request reduced fund commitments. The GP has no obligation to comply with the requests, but they may voluntarily do so to build goodwill for future opportunities.
2. Agreement termination. In extreme cases, the LPs can form a collective agreement and terminate the GP without cause and without recourse. This path will significantly damage the GP’s reputation. As such, either a threat of termination or noise of LP dissatisfaction can generate a response from the GP.
‘–
Outside governance
1. Refusal to commit to follow-on funds. The easiest way to show dissatisfaction with a manager’s performance is to not invest in follow-on funds. Managers fear this action because it makes raising capital more difficult and may tarnish their reputation.
2. Investor default. Rather than making an explicit vote of no confidence, an investor could decline to supply previously agreed-upon capital when a commitment is called. This is known as a default. While effective in the short run, this option holds risk for the investor. The LP is contractually obligated to provide committed funds. If they default, then they may lose all prior invested capital, and they may also lose access to private markets as word could spread to other GPs that a given LP defaulted.
3. Secondary market divestment. An LP could also consider finding a buyer on the secondary markets to assume their position and remaining commitments.
5.4 - Hedging, Rebalancing, and Monitoring
