Volume 2 Flashcards
Put-Call Parity ?
typiquement on ignore pv(X)
Put-Call-Forward Parity ?
typiquement on ignore pv(X)
Synthetic Long ?
Long Call, short Put.
Same X strike, same expiration date.
= hedge an existing short position or to arbitrage mispricing.
such a strategy would be implemented by an investor who has a bullish view of the market and an expectation that implied volatility will remain unchanged.
Synthetic Short ?
Long put, short call.
Same X strike, same expiration date.
= hedge an existing short position or to arbitrage mispricing.
Covered Call ?
Long underlying Stock, short Call.
a covered call, is appropriate if the expectation is that volatility of the underlying will be lower than the implied volatility of the call option.
What do we use a covered call for ?
1) yield enhancement:
receive premiums when limited upside in uderlying is expected.
If called away, results in a tax event.
2) Position reduction:
sell ITM calls (caution for tax mismatches)
3) Position exit @ target price = SELL CALLS @ target price.
Protective Put (max g&l, value @ expir, profit @ expir) ?
Breakeven price = S0 + p0
If Δ of our position > 0, when do we benefit ?
Else, if Δ < 0 ?
If Δ>0 = benefit from price increase of S0.
If Δ<0 = benefit from price decrease of S0.
What asset is positive delta ? Negative delta ? neutral delta ?
+Call: Δ>0
+ Put: Δ<0
+S0: Δ=1.
S0 movements impact on the delta of a covered call position ?
Covered call = long S0 (Δ=1); short C0 (Δ<0).
Donc as S0↑, short call Δ –> -1; covered call pos Δ –> 0.
As S0↓, short call Δ –> 0; covered call pos Δ –> 1.
S0 movements impact on the delta of a protective put position ?
Protective Put = long S0 (Δ=1); long S0 (Δ<0).
Donc as S0↑, long put Δ –> 0; protective put pos Δ –> 1.
As S0↓, long put Δ –> -1; protective put pos Δ –> 0.
What if we get a forward instead of an option to replicate a protective put or a covered call ?
Alors on remplace notre position sur S0 par F0. And the Forward will have a delta equal to the stock position.
!!!NOTABLE DIFFERENCE WITH OPTIONS!!! :
The delta of a forward position doesn’t change, unlike the one an option position (covered call/protective put).
Compare the effect of buying a call with the effect of selling a put; on a short underlying S0 position.
Bull Spread ?
Maximum profit per share of bull call spread = (XH – XL) – (cL – cH).
Bear Spread ?
Breakeven share price is calculated as XH – (pH – pL) = €31.00 – (€3.00 – €0.50) = €28.50.
long Straddle ?
long
short straddle ?
Strategy 7: Writing both the April €75.00 strike call option and the April €75.00 strike put option on XDF
The maximum gain is €5.76 per share, which represents the sum of the two option premiums, or c0 + p0 = €2.54 + €3.22 = €5.76. The maximum gain per share is realized if both options expire worthless, which would happen if the share price of XDF at expiration is €75.00.
Short straddle use case ?
the outlook is for the market to trade in a narrow range and an increase in implied volatility is expected.
Collars ?
protective put + sell a call = p0 - c0
You buy P0 with the money you get from selling C0 usually (= zero-cost collar).
Objective = limit downside loss of S0 with the long put, by cutting potential gains with the short call.
What’s a calendar spread ?
Buy and Sell the same type of option, but with different expiration dates.
Can be done with calls and puts.
Long Calendar spread ? Short calendar spread ?
1) Long Calendar Spread:
Sell near-term option, Buy long-dated Option.
2) Short Calendar Spread:
Buy near-term option, Sell long-dated Option.
When is gamma the largest ?
The largest gamma occurs when options are trading at the money or near expiration, when the deltas of such options move quickly toward 1.0 or 0.0. Under these conditions, the gammas tend to be largest and delta hedges are hardest to maintain.
Volatility skew&smile ?
y axis = implied volatility
x axis = strikes X of calls and puts @ different prices.
Increased implied volatility of options ET more OTM calls bought = DRAWS A VOLATILITY SMILE @ t+1 = BULLISH.
Historical volatility ?
Increase in Skew & Implied Volatility ?
If you have no increase in OTM calls buying AND increase in implied volatility = INCREASE IN SKEW = BEARISH.
What is a long Risk-reversal strategy ?
If we believe implied volatility of OTM PUTS is overpriced VS Implied vol of OTM CALLS.
To delta hedge the option position, we can sell the underlying asset S0.
Short risk reversal use case ?
This strategy would be implemented to benefit from an implied volatility skew.
Term structure of volatility ?
ATTENTION!!!!!
A LT sur la courbe bleue, ca peut repiquer vers le haut, parce que le futur peut être volatile même si le ST est volatile aussi (et on a donc un smile ou le mid-term est le moins volatile).
Options strategies matched with investment objectives and expected estimates of markets (implied vol, underlying S0) ?
Demonstrate how interest rate swaps can be used to modify a portfolio’s risk and return.
A pay-fixed, receive-floating swap has a negative (positive) duration from the perspective of a fixed-rate payer (receiver), because the duration of a fixed-rate bond is positive and larger than the duration of a floating-rate bond, which is near zero.
Moreover, the negative duration of this position to the fixed-rate payer/floating-rate receiver makes sense in that the position would be expected to benefit from rising interest rates.
Adjusting a Portfolio Duration (int swap) ?
Demonstrate how forwards can be used to modify a portfolio’s risk and return.
FRAs can be customized (OTC) and have counterparty risk.
Demonstrate how futures can be used to modify a portfolio’s risk and return.
Same as FRAs, but futures are exchange-traded and cash settled.
Eg. Eurodollar Futures –> Underlying = ref. rate on $1M (quoted on index basis: 100 - ref rate).
Fixed income futures –> Underlying is a generic GOV Bond.
Adjusting PF duration (Futures) ?
CTD = cheapest to deliver
BPV Target ?
BPV de n’importe quoi ?
Adjusting PF duration COMPLETE HEDGING (Futures) ?
B is correct. The basis point value of Portfolio A (BPVP) is $130,342.94, and the basis point value of the cheapest-to-deliver bond (BPVCTD) is $127.05 with a conversion factor of 0.72382. The basis point value hedge ratio (BPVHR), in the special case of complete hedging, provides the number of futures contracts needed, calculated as follows:
BPVhr= (−BPVpf / BPVctd) × CF
= (-$130,342.94 / $127.05) × 0.72382 = −742.58
Demonstrate how currency swaps, forwards and futures, can be used to modify a portfolio risk and return.
To manage a currency exposure:
Currency swap = notional exchanged at beg. and end of period; @ a fixed rate (no currency risk). Periodic interest pmts are exchanged (currency risk).
EG: A CANADIAN company enters a currency swap with an US.
1) @Inception = CANADIAN pays the notional principal of CAD and will receive an amount of USD according to the USD/CAD exchange rate
2) @each swap payment date = CANADIAN will receive interest in CAD and will pay interest in USD. Both payments are based on floating reference rates for their respective currencies. The CAD rate will also include a basis rate that is quoted separately.
In other words, on each settlement date, CANADIAN will receive an amount of CAD based on the CAD floating rate minus the basis rate applied to the swap notional value, and it will pay an amount of USD based on the USD floating rate and the USD/CAD exchange rate that was set at inception.
3) @maturity = The cash flows at maturity are the inverses of the cash flows at inception
Cross-currency swap (basis) ?
Demonstrate how currency forwards and futures, can be used to modify a portfolio risk and return.
Down the rate = divide.
Up the rate = multiply.
Demonstrate how equity swaps, forwards and futures, can be used to modify a PF risk and return.
Equity swap types ? Total Return swap ? what is the underlying ?
pay equity, receive floating/fixed/equity.
- Total Return swap = includes dividends.
- Underlying can be a single stock, a basket of stocks, or a stock index.
How to reduce stock market exposure ?
equity swap: rec fixed/floating; pay equity.
How to diversify a concentrated equity position ?
Equity swap: receive equity INDEX return;
pay single stock equity return.
Equity futures & forwards: what if the underlying is an equity index ? What if the underlying is a single equity stock ?
Index = Then the futures/fwd is cash settled
Single stock = then cash or physical settlement.
If the swap is physically settled, on the termination date, the equity swap receiver will receive the quantity of the single stock specified in the contract and pay the notional amount. Because Tryon wants to keep the shares (and not sell them to provide the notional amount), a cash-settled total return payer swap is an appropriate strategy that hedges the equity position in Inwood.
N° of equity futures contract / Currency futures so that we can hedge ourselves ?
How to change the β of a PF (avec des futures) ?
N° of equity futures contract we need to achieve the desired β.
Cash Equitization ?
βcash = 0.
demonstrate the use of volatility derivatives and variance swaps.
Being Long Volatility can be a hedge against a Long Equity PF (because when markets drop, volatility tends to increase).
Volatility futures & options ?
Term structure of volatility ?
Variance Swap ?
Settlement amount of a Variance Swap @ T ?
Variance strike price is the implied volatility of a put such that (put strike/index strike) = 90%
Settlement amount of a Variance Swap @ t ?
pvf is present because the settlement amount needs to do be discounted from time T to t.
Exemple de variance swap stlmt amount @ t ?
inferring MKT expectations ?
Typical end-of-month (EOM) activity by large financial and banking institutions often induces “dips” in the effective federal funds (FFE) rate that create bias issues when using the rate as the basis for probability calculations of potential Federal Open Market Committee rate moves. If EOM activity increases the price for the relevant fed funds contract, the FFE rate would decline. A decline in the FFE rate would decrease the probability of a change in the fed funds rate. To overcome this EOM bias, data providers have implemented various methods of “smoothing” EOM dips.
Proba of change in Fed funds rate ?
a = 1.5%
b = target rate.
(B = bank rate = upper; O = overnight rate = lower).
c = 2.875% if previous range was 2.5% - 2.75% and 25bps increase proba test (with new range, midpoint = (3% + 2.75%) / 2)
to derive probabilities of Fed interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the FFE rate—that is, the rate that depository institutions actually use for lending to each other, not the Fed’s target federal funds rate. The underlying assumption is that the implied futures market rates are predicting the value of the monthly average FFE rate.
What is the “basis risk” ? How to arbitrage bond futures using the basis risk ?
If the basis is positive, a trader would make a profit by “selling the basis”—that is, selling the bond and buying the futures. In contrast, when the basis is negative, the trader would make a profit by “buying the basis,” in which the trader would purchase the bond and short the futures.
basis risk or spread risk—the difference between the market performance of the asset and the derivative instrument used to hedge it. When using an interest rate swap to hedge, it is possible that the changes in the underlying rate of the derivative contract, and thus in the value of the swap, do not perfectly mirror changes in the value of the bond portfolio = imperfect substitutes
Effective interest rate of a loan ?
= Rate - Hedge gain.
Hedge gain = contract sold - contract unwinded
Analyze the effect of currency movement on PF return.
R dom curr PF
Exemple domestic PF return avec currency movements.
R dom curr PF, avec multiple foreign currencies ?
Variance of PF in dom curr, containing foreign currencies ?
Diversification considerations with regard to currency management ?
1) Time Horizon:
- @ LT, currencies mean revert (to Fair Value Equilibrium or historical AVG)
- @ ST, currencies are Random Walks.
2) Asset Composition:
- R_forCap of different asset classes have different CORREL_(RforCap, RforCurr).
- Greater CORREL for fixed income VS equity = currency exposure provides little diversification benefit to fixed income.
3) Cost Considerations
a) trading costs
b) opportunity costs (= forgo favorable foreign curr moves)
4) Currency risk Spectrum (Passive; Discretionary Hedging = tight risks limits; Active Currency MGMT = looser risk limits; Speculation)
5) Currency overlay currency ACTIVE MGMT (currency alpha) is outsourced; whereas currency hedging (currency beta) is internalized.
Hedging trading costs ?
Compare Active Currency trading strategies based technical analysis.
Technical Analysis = very common in Currency MKTS
Describe how changes in factors underlying active trading strategies affect tactical trading decisions:
Forward rate bias of carry trades (for hedging purposes) ?
- Buy currencies selling @ forward discounts.
- Sell currencies selling @ forward premiums.
Net short volatility ? Net long volatility ?
Describe how forward contracts and effects of foreign exchange swaps are used to adjust hedge ratios.
static hedge ?
Describe how forward contracts and effects of foreign exchange swaps are used to adjust hedge ratios.
Dynamic hedge ?
Describe how forward contracts and effects of foreign exchange swaps are used to adjust hedge ratios.
options to hedge ?
If we use forwards, long base in S_P/B = sell base forward to hedge.
With options, buy ATM put on S_P/B.
Basis risk ? Roll yield ? Premia income ?
Cross-hedge most important factor ?
Describe the use of cross-hedges in PORTFOLIOS exposed to Multiple foreign currencies.
Cross hedge = a position in one asset is used to hedge the risk exposure in another.
Describe the use of minimum variance hedge ratios; in PORTFOLIOS exposed to Multiple foreign currencies.
Minimum Variance Hedge Ratio = typically used for indirect hedges (introduces basis risk, like for all cross-hedges je crois).
HR hedge ratio = regression of the return on the assets to be hedged against the return on the hedging asset (c’est un β).
Discuss challenges for managing emerging MKTS currency exposures.
some EM currencies, the broker might not let you enter in a trade with them because he can’t actually deliver the currency to you (non-deliverable).
NDF & CFDs ?
Describe Fixed Income Portfolio measures of risk & return, as well as correlation characteristics.
- Pour ModDur, on divise par le periodic CF yield du PF (pas the weighted avg CF yield of each bond) !!!!!
- EffDur –> Le Δcurve est model derived; alors que pour empirical duration, baaah c’est empirique.
Avg ModDur of bonds in the bond PF ?
Avg EffDur of bonds in the bond PF ?
Avg Convexity of bonds in the bond PF ?
Avg EffConvexity of bonds in the bond PF ?
Describe Fixed Income Portfolio measures of risk & return, as well as correlation characteristics (spread duration; dts; PF dispersion).
- DTS = duration times spread
- Portfolio dispersion = weighted avg variance of the time to CF with respect to MacDur –> The greater the PF dispersion, the greater the convexity of the PF.
Describe bond market liquidity, including the differences among market subsectors, and discuss the effects of liquidity on fixed income Portfolio Management.
MARKET LIQUIDITY???
Describe bond market liquidity, including the differences among market subsectors, and discuss the effects of liquidity on fixed income Portfolio Management.
DIFFERENCES AMONG SUBSECTORS?????
Describe bond market liquidity, including the differences among market subsectors, and discuss the effects of liquidity on fixed income Portfolio Management.
EFFECTS OF LIQUIDITY ON FI PF MGMT ????
+ 3) Alternatives to Direct Investing in Bonds
- Derivatives (exchange-traded and OTC), ETFs, Mutual Funds
–> Generally more liquid than underlying.
Describe & Interpret a model for Fixed-Income Return.
–> Decompose FI Return.
note: for a corporate risky bond, for the change in spread component, if it’s a floating rate Note, we use -Spread Duration and not -ModDur in the formula.
Rolling yield (fixed income) ?
= coupon + rolldown return
The roll down return is equal to the bond’s % price change, assuming an unchanged yield curve over the strategy horizon. The roll down return results from the bond “rolling down” the yield curve as the time to maturity decreases. As time passes, a bond’s price typically moves closer to par.
Currency MGMT roll yield ?
Discuss the use of leverage, alternative methods for leveraging, and risks, that leverage creates in Fixed-income PORTFOLIOS.
Rp with leverage for FI PF ?
Discuss the use of leverage, alternative methods for leveraging, and risks, that leverage creates in Fixed-income PORTFOLIOS.
Methods of gaining Leverage (part1) ?
Discuss the use of leverage, alternative methods for leveraging, and risks, that leverage creates in Fixed-income PORTFOLIOS.
Methods of gaining Leverage (part2) ?
The rebate rate flows back to the BORROWER.
Discuss differences in managing Fixed-Income PFs for taxable and tax-exempt investors.
(pour les taxable investors)
If the cap gains in a fund are not pass-through taxed, then you would be taxed on it when you resell you shares (on your total cap gain since inception)
Describe liability-driven investing.
= Managing Assets to meet given Liabilities.
Evaluate strategies for managing a single liability (= Type 1 Liab) = Immunization.
1) Use a ZERO CPN BOND = Done!
2) Using CPN Bonds –> Price & Reinvestment (= variance in the realized RoR: requires the MGMT of Duration).
Solution = picture.
*PV_pf(CFs) = MV(Assets); et a = assets.
What is immunization ?
Immunization is the process of structuring and managing a fixed-income portfolio to minimize the variance in the realized rate of return and to lock in the cash flow yield (internal rate of return) on the portfolio.
= ZERO REPLICATION
ZCB, bullet, barbell (dispersion around investment horion) ?
When matching MacDur_a with MacDur_liabs; we must use the correct measure of MacDur @ the PF Level !!!! (not @ the level of weighted individual Assets).
*MacDur_PF = Invest Horizon in all 3 cases, only dispersion varies.
What is structural risk ?
normalement on match la MacDur_PF avec MacDur d’un ZCB (pas macdur du bond coupon paying en question) .
Pour minimiser structural risk, use a laddered bond PF or bullet PF (concentration of bonds’ durations, not dispersed like with a barbell strcuture).
Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation.
CASH FLOW MATCHING.
Li = liability que l’on doit payer.
Ci = coupon.
Bi = PAR Value Bond.
Describe construction, benefits, limitations and risk-return characteristics of a LADDERED BOND PF.
good for liquidity mgmt
Evaluate Liability-based strategies under various interest rate scenarios, and select a strategy to achieve a PF’s objective.
DURATION MATCHING, MULTIPLE LIABS: conditions to meet ?
For duration matching, these are the conditions that we need to meet.
*PV(liabs) = discounted by CF yield of PF.
BPV = basis point value.
Evaluate Liability-based strategies under various interest rate scenarios, and select a strategy to achieve a PF’s objective.
DURATION MATCHING, MULTIPLE LIABS, but you typically don’t focus on the conditions to meet but on liquidity, safety, and potentially return ?
DERIVATIVES OVERLAY, tool to DURATION MATCHING.
Ultra 10yr bond = 9.5-10 yrs
Duration gap = BPV(L) - BPV(A)
Evaluate Liability-based strategies under various interest rate scenarios, and select a strategy to achieve a PF’s objective.
Contingent immunization ?
Surplus can be positive or negative.
Threshold is not necessarily 100%, the threshold might be that MV(A) is 95% of MV(liab).
Evaluate Liability-based strategies under various interest rate scenarios, and select a strategy to achieve a PF’s objective.
Interest Rate Swaps ?
axe y c’est gains/losses.
axe x c’est interest rate.
Evaluate Liability-based strategies under various interest rate scenarios, and select a strategy to achieve a PF’s objective.
Interest Rate Options ?
axe y c’est gains/losses.
axe x c’est interest rate.
BUY receiver swaption gives the right to enter into a RECEIVER FIXED SWAP.
Swaption collar ?
if interest rates are expected to rise
IR anticipation strats
Explain risks associated with managing a PF against a liability structure.
1) Model risks
–> Whenever assumptions are made about future events & approximations are used to measure Key parameters (eg. Defined Benefit Pension plans)
2) measurement errors exist for passive immunization strategy (including Type 1 cash flows)
3) Assuming that Δyields are equal for A, L & Hedging Instruments
7) Asset Liquidity
–> for Contingent immunization approach, if active strategies fail.
Discuss bond indexes, and the challenges of managing a fixed income portfolio to mimic characteristics of a bond index.
Pure indexing ? Enhanced indexing ? Active Mgmt ?
enhanced indexing = deviations on secondary risk factors, mais match primary risk factor (eg. duration).
Discuss bond indexes, and the challenges of managing a fixed income portfolio to mimic characteristics of a bond index.
Challenges of benchmarking ?
Less than 1% of bonds trade daily.
+ Index composition changes frequently (maturities, callability, new issues, etc.)
Primary Risk Factors ?
Alternative to matching Key Rate durations (callable/non-callable) ?
Compare alternative methods for establishing bond market exposure PASSIVELY.
DIRECT PASSIVE INVESTING ?
Alternatives to Direct investing (still passive) ?
bond ETFs can trade at discounts to their underlying indexes, and those discounts can persist (because illiquid bonds).
Total return swaps = low transaction costs and initial cash outlay VS bond mutual funds
Discuss criteria for selecting a benchmark and justify its selection.
DAILY VALUATION, not WEEKLY.
bond issuer propensity & preferences –> eg. Rates are very low, donc les companies font issue debt, et surtout LT.
Donc the Index will reflect there are more LT bonds, donc la duration de l’index va augmenter.
Donc on doit matcher cette augmentation de la duration, those LT new issuances.
