Lecture 4: Section 1

Lecture 4: Section 1

Generic Currency Signals

Momentum or Trend: bet on continuation of directional moves

Many ways to calculate the autoregressive nature of currency returns

• BofA: use past month and

• Deutsche Bank: use last 12-month returns and buy top-3 and sell bottom-3

• Could use MA cross-over rules (like 20-day & 200 day)

Why (and when) should momentum strategies work?

1

1

ln / 0

ln / 0

t t

t t

long foreign currency if S S

short foreign currency if S S

Carry: long high interest rate, short low interest rate

What interest rate differential?

• BofA: use 1 month LIBOR

• Deutsche Bank uses 3 month LIBOR & buy top-3 & sell bottom 3 – Rebalance every 3 months

How can you manage the risk of carry unwinds?

for usd

for usd

buy foreign currency if r r

sell foreign currency if r r

Fundamental Value: bet on reversion to long-term equilibrium value

Purchasing Power Parity (PPP) is most common measure

• BofA: compare PPP, adjusted by return to carry, to current spot rate

• Deutsche Bank: buy top-3 undervalued currencies and sell top-3 overvalued currencies

– Valuation determined by OECD PPP versus current spot rate

When will PPP be most likely to add value?

for usd

for usd

r r

r r

Buy foreign currency if PPP e S

Sell foreign currency if PPP e S


Liquidity Considerations

How do currencies rank in terms of liquidity?

0

20

40

60

80

100

EURUSD GBPUSD USDJPY EURCHF USDCHF AUDUSD EURSEK USDCAD EURNOK NZDUSD

What do you do about liquidity differences?

BofA has a “most liquid” portfolio:

• USD, EUR, JPY, GBP, CHF

And a less liquid portfolio:

• AUD, CAD, NOK, NZD, SEK

Can impose position caps that reflect liquidity tiers

• Depends upon size of portfolio

Could use IC weighting to alter alphas

*alpha IC volatility score

Modeling transaction costs

Liquidity will determine market impact of trades

• If you have large portfolio will have “backlog” where actual positions differ from desired positions

• Tcosts affected by inventory risk to broker (G&K, Ch. 16)– Estimated time for opposing trades to match a trade of size V:

• Trade 1 day’s volume, expect it to take a day for counterparties to clear risk

– Inventory risk facing liquidity provider depends on volatility:

• Convert annual vol to vol over relevant horizon for inventory management

• Measure in units of days, with 250 trading days in year

clear

Vtrade

Vdaily

250clear

inventory


• ADV varies across currencies– Use BIS survey data

• Vol varies across currencies– Calculate trailing vol or use implied vols

• Smooth some to avoid vol spikes distorting relative costs

• Beyond market impact costs, have fixed costs of commissions and spreads

i i i

tradesizetcosts a

ADV


Objective function:

• Tcost amortization factor– Higher to trade patiently– Lower to trade faster– Could simulate model to find “optimal” TCAF

• Experience with backlog will guide

• How often to rebalance? – Could use calendar interval or backlog risk trade trigger rule

• Only trade when risk >threshold

' ' | |th h Vh TC h

'

backlog opt act

backlog backlog backlog

h h h

h Vh


Risk Modeling

Risk modeling: drawdown risk

Clients often want to think about extreme value risk

• What is maximum drawdown? – Duration and magnitude

– Experience for fund with history

– Simulation for start-up

– Could make part of every proposed signal diagnostic

• Investment officers have different horizon than fund might suggest– Insurance companies or pension funds have very long-run horizon?

• Investment officer bonus paid annually• A major drawdown can get you fired

Risk modeling: covariance model

Fast or slow, historic or forward-looking?• Speed of COV should match rate of model alpha decay• Do you want “normal” correlations across assets?• Do you want to capture short-term shifts in correlations?• Do you want slowly-evolving correlation matrix?

– Exponentially smoothed with long HL

– Just update once-a-month?

– Impose priors in a “shrinkage” matrix to help capture important relations• Look at “hedge bundles” implied by construction: AUD & NZD; NOK & SEK;

EUR & CHF; ………• Regional funding; commodity currencies; “flight to quality” currencies;…..

• A fast model would require a faster COV matrix– Update daily

– Use implied vol only or in a blend with historic

Realized Volatility: the most accurate predictor

• Compute daily vol from the sum of squared intradaily returns– Motivated by approaching limit of Brownian motion

– Consider a continuous-time log process for the quote q:

– The corresponding discretely-sampled returns are:

– The variance of the h-period returns is:

– While that variance is unobservable, a measure of realized vol that is consistent (in m) for the integrated vol is summing the high-frequency squared returns:

Realized Volatility: the most accurate predictor

• Don’t sample at very highest frequency as get “microstructure noise”– Non-synchronous prices

– Data holes

• Can treat volatility as observable rather than latent – See Melvin & Melvin (Review of Economics & Statistics, 2003) for FX

example

• Use daily vol estimates to construct cov matrix– Better for fast models than implied vol, which contains risk premium


Model Building Tips

Follow SPCA Method for signal development

Sensible– First step is to convince yourself (and others) that the idea makes sense– No data mining allowed! – If it conflicts with finance theory, why?

Predictive– The proposed signal is useful for predicting returns

Consistent– Performance occurs through time (not in 1 episode)– May like signal that is not very consistent, but in certain market

conditions adds good diversification• For instance, a value signal that only has positive performance when carry

unwinds

Additive– Does it add value beyond existing model?

Useful Diagnostics for Signal Development

• IR for whole backtest sample and subsamples

• Cumulative return plot

• Drop one asset at a time to determine dependence across assets

• Lead-lag plots of IR around implementation day– Determine speed of alpha decay – Inform trading process: what do you lose by trading patiently?

• Tilt-timing analysis– Tilt: what if we held a constant portfolio– Timing: residual of actual returns - tilt

'

' '

tilt hr

timing hr hr


Pojarliev & Levich, Do Professional Currency Managers Beat the Benchmark?

Currency Benchmark

• There is no accepted practice– There is no “market portfolio”

• All positions long/short

– Zero assumption from random-walk findings of academic literature

– Cash: if you can’t beat that, why invest?

• P&L create currency indexes off of generic signals– Are these benchmarks?

– More like style betas

Estimate factor model

• Returns from Barclay Currency Trader Index (BCTI)

• 1 month LIBID for risk-free returns

t i it ti

t

R F

R excess return total return riskfree rate

skill

factor loading

F beta factor

Style Factors

• Carry– Citi G10 Carry Index: equally-weighted basket of 13 pairs

• Trend– AFX index: equally-weighted portfolio of 3 MA rules

• 32, 61, 117 days over 7 pairs weighted by turnover

• Value– Citi Beta1 G10 PPP Index: long currencies <20% undervalued & short

currencies >20% overvalued• OECD PPP for 13 pairs compared to spot

• Volatility– Avg of implied vol for EURUSD & USDJPY

• This is relevant for vol strategies rather than directional bets• But will capture carry unwinds so would want to be long JPY & short high-

yielders

All manager index results

• Trend is useful factor; carry & PPP not useful

• Alpha insignificant when factors are accounted for

• Short sample results– Carry sigificant 2001-2006 but Trend dominates

– Vol significant in both periods, but more significant in latter period• They say currency derivatives trading increased after 2001• In the low vol period, selling vol was a successful strategy

– Vol quite low until 2007, I kept saying “just wait”

Individual Manager Results

• 34 have data over 2001-2006 period (survivors)• Alpha positive on avg with big range

– Reflects different risk levels of funds

• IR puts on equal footing– Mean=0.47; median=0.45

• Estimate IR from 4-factor model– Only 8 firms have sig & positive alpha

– So returns are combination of beta & alpha

– With similar returns, find some managers generative beta while others generate alpha

– Trend sig for 15 firms; Carry for 8; Vol for 7; Value for 5• Firms have different approaches

Timing Ability, Alpha & R-square

• A passive portfolio has asset weights uncorrelated with returns– Regress returns on factors and factors squared

– Some evidence of timing ability for about ½ of firms

• Finally, the more a firm loads on 4 factors, the smaller alpha

Critique

• Don’t believe that it is cheap & easy to get active manager performance by just betting on generic strategies– Active managers adjust portfolio to changing market conditions

• Putting a generic strategy on cruise control is very dangerous– 2007 was good lesson for carry indexers

• Paper has small sample of active managers & conclusions are too sweeping from this limited universe

Documents

Lecture 4: Section 1