SAA vs TAA
SAA: Combines CMA (return, std, correlation) with an investor's risk, return, and investment constraints (IPS)
TAA: active management where managers deviate from the SAA to take advantage of short term opportunities
ALM Definition
Asset Only Definition
ALM: Tailoring asset alloication to meet liabilities and maximize surplus (high fixed income)
Asset Only: only focus is highest return for risk taken
Dynamic vs Static Asset Allocation
Dynamic: multiperiod view (one period affects others)
Very difficult and costly to implement
↓ transaction costs
ALM uses Dynamic
Static: Use inputs at a point in time and build a longterm allocation
Required Return Geometric Calculation
(1 + r)(1 + r)(1 + r)  1
Example:
Foundation needs 4% for distributions, inflation is 3%, fees are 0.5%.
(1.04)(1.03)(1.005)  1 = 7.66%
UtilityAdjusted Return
U_{P} = R_{p}  .005(A)(std_{p})^{2}
A = risk tolerance score 18. (8 being most risk adverse)
Example: risk score of 5, choose best portfolio
Portfolio A r = 11.5%, std 18% 11.5  0.005(5)(18)^{2} = 3.4
Portfolio B r = 8.%, std 14% 8  0.005(5)(14)^{2} = 3.1
Portfolio C r = 6.0%, std 10% 6  0.005(5)(10)^{2} = 3.5
Select C
Roy's Safety First Measure
RSF = (R_{p}  R_{MAR}) / std_{p}
R_{MAR} = minimum acceptable return
Example: Wants to minimize chances to earn less than 3.5%
Portfolio A r = 11.5%, std 18% (11.5  3.5) / 18 = 0.44
Portfolio B r = 8.%, std 14% (8  3.5) / 14 = 0.32
Portfolio C r = 6.0%, std 10% (6  3.5) / 10 = 0.25
Select A
Shortfall Risk
Semivariance
Shortfall risk = risk of exceeding a maximum acceptable dollar loss
Semivariance = bottom half of the variance (only using returns below expected return)
Asset Class Approprately Specified
 Assets in the class are similar (statistical and descriptive)
 Asset classes are not highly correlated
 Individual assets only in ONE class
 Mostly liquid assets
 Cover majority of all possible assets
When should an additional asset class be added to an existing portfolio?
If S_{i} > S_{p} * cor_{i,p}
Remember: Sharpe = (r  R_{f}) / std
Example 1:
Sharpe ratio: P = 0.41, Inv1 = 0.30, Inv2 = 0.31, Inv3 = 0.19
Cor with P: Inv1 = 0.77, Inv2 = 0.80, Inv3 = 0.40
Inv1: S = 0.30, 0.41 * 0.77 = .316  DONT add
Inv2 S = 0.31, 0.41 * 0.80 = 0.328  DONT add
Inv3 S = 0.19, 0.41 * 0.40 = 0.164  ADD
Example 2:
Rf = 3%, Portfolio R = 12%, Std = 18%
New Investment R = 12%, Std = 30%
1. Sharpe ratio A (123)/18 = 0.5, Sharpe B (123) / 30 = 0.3
2. S_{i} = S_{p} * cor_{i,p} 0.30 = 0.50 * cor_{i,p}
3. Solve for cor_{i,p} = 0.30/0.50 = 0.60
If correlation is 0.60 sharpe is unchanged
If correlation is less than 0.60 adding will increase Sharpe
If correlation is more than 0.60 adding will decrease Sharpe
Nondomestic Equity and Bonds Risk
 Currency risk (reduced by low correlation)
 Political risk
 irresponsible fiscal/monetary policy
 lacks legal and regulatory rules
 Home country bias
 Higher costs or less liquid
 irresponsible fiscal/monetary policy
 lacks legal and regulatory rules
Contagion/Conditional Correlation
Lower correlations for normal conditions
HIgher correlations during market crises
MVO Strengths/Weaknesses
Strengths
Identifies portfolio with highest expected return for risk
Widely available and understood
Drawbacks
Must specify all returns (input bias)
Tends to select concentrated allocations
CML
CML: Line between R_{f} and the market portfolio
If an investor can borrow and lend at R_{f} all portfolios on the CML dominate the normal EF
Drawbacks:
 Hard to find a R_{f} asset over multiple periods
 Borrowing increases risk
Resampled EF
Running MC on all portfolios to get a range. Then take the average
Advantages:
 More stable EF (but it does fall below original frontier)
 Considered more diversified
 Can see a range of what assets can be held. (Less turnover)
Diadvantages:
 Lack of sound theoretical basis
 Based on historical data
BlackLitterman
Addresses instability issues
Two Models:
 UBL Model  unconstrained (can shortsell).
 BL Model  no short selling
 Take consensus return expectations (global market index)
 Manager adjusts asset class weights based on his opinion
 Runs the MVO again
If an asset class increases return, it will have more weight.
BlackLitterman Pros and Cons
Pros
Starting with a global portfolio generally produces a well diversified portfolio
Reduces input bias
Cons
Complex and utilizes historical std
Asset Liablity Management for MVO
 ALM searches for allocations that maximize the surplus between assets and liabilities
 MSVP = Minimum Surplus Variance Portfolio (could be negative)
 Choosing above the MSVP is a beta decision
 Can combine ALM with BL or resampling
ExperienceBased Techniques (EBTs)
 Process of elimination, "rules of thumb"
 Starts with a 60/40 and then adjust based on risk tolerance and time horizon
Corner Portfolios
Definition: A portfolio on the EF
Three criteria of a corner portfolio:
 Must be a portfolio on the EF
 To identify: asset class weight from + to 0 or 0 to +.
 Global minimumvariance portfolio (GMVP)  the bottom left corner portfolio
Using 2 portfolios to construct another
Step 1: solve for the return and weights
R_{p} = w_{B}(R_{B}) + (1  w_{B})(R_{A})
Step 2: calculate the weighted average of the std
Example:
Portfolio A: 10% return, 12% std, Portfolio B: 15% return 16% std
Construct a portfolio with an 11% expected return:
Step 1: 11 = w_{B}(15) + (1  w_{B)}(10)
11 = 15w_{B} + 10  10w_{B}
1 = 15w_{B}  10w_{B}
1 = 5w_{B}
1/5 = 20% into portfolio B
CAL (Capital Allocation Line)
CAL: Line between Rf and the tangency portfolio (portfolio with highest Sharpe ratio)
1. If required return f
2. If required return > tangency: use margin to leverage return
Basically says you can borrow to get up to the CAL line
CAL Formula
Rp = w_{t}(R_{t}) + (1  w_{t})(R_{f})
t is for tangent portfolio. Same as CP formula except R_{f}
Example:
Allocate between tangent portfolio E and R_{f} of 2% to meet return target of 8.7%
5.61W_{e} + 2(1  W_{E}) = 8.7
3.61W_{E} = 6.7
W_{E} = 1.86 This means borrow 86% to invest
Currency Exchange Details
1. Bid: price to buy
2. Offer (ask): Price to sell
3. Spread: Difference between bid and ask
AKA: PIPS > They are stated in the 10,000
4. Bid = 1/ask Ask = 1/bid
Currency Saying
Going up = bid (multiply)
Going down = ask (divide)
Use the % from the top currency
Note: $1.55 per E1 means: 1.55 USD (quote) 1 E (base)
So USD is domestic, E is foreign
Forward Points
Adjustment to the spot price to determine forward price
**move decimal right by same # of decimal places shown
Spot FP Points w/ Decimal Forward Price
1.33 1.1 1,1/100 = 0.011 1.33 + 0.011 = 1.341
2.554 9.6 9.6/1000 = 0.0096 2.5540.0096=2.5444
0.7654 13.67 13.67/10000=0.001367 .7654+.001367=0.766767
What is an FX Swap?
Rolls over a maturing forward contract using a spot transaction (2 days prior to expiration)
Step 1: offset the maturing contract
Step 2: Enter a new forward contract
Option Basics (Call & Put)
 Call: right to buy
 gains when underlying rises above strike price (delta approaches 1.00)
 Put: right to sell
 gains when underlying falls below strike price (delta apporaches 0.00)
 gains when underlying rises above strike price (delta approaches 1.00)
 gains when underlying falls below strike price (delta apporaches 0.00)
Currency Options Means What?
A call on one currency and a put on the other
Always for the base currency
Example: A put option to sell 100,000 at MXN/EUR at 20.1
1. Right to sell 100,000 EUR and buy 2,010,000 MXN
2. Right to buy 2,010,000 MXN and sell 100,000 EUR
Currency Trading Option Strategies

Buy ATM put; removes downside risk and retains upside (high cost)

Buy OTM put; remove some downside risk and returns upside

Buy high strike put and sell low strike put
 downside protection between strikes, retains upside

Collar (sell a call and buy a put); downside protection to put strike, upside only to call strike

Seagull (buy high strike put, sell low price put, sell OTM call)
 downside protection between put strikes, upside only to call strike
 downside protection between strikes, retains upside
 downside protection between put strikes, upside only to call strike
Currency Option Relationships
Price of Base ^ Call Option Put Option
From 0 > Strike OOM and rising ITM and falling
Delta 0.00 > 0.5 Delta 1.0 > 0.5
To Strike ATM ATM
Delta at 0.5 Delta at 0.5
Strike > upward ITM and rising OOM and falling
Delta 0.5 > 1.0 Delta 0.5 > 0.00
Domestic and Foreign Currency Definitions
 Domestic (home) currency: investor's currency that is reported
 Foreign (local) currency: all currency's outside of domestic
 R_{FC} = local market return
 R_{FX} = local currency return (% change)
 R_{DC} considers both local market and currency returns
Domestic Currency Return Formula
R_{DC} = (1 + R_{FC})(1 + R_{FX})  1
Note: foreign currency must be the base currency
Example:
1 year EUR increased 5% and exchange rates went from 1.300 USD/EUR to 1.339 USD/EUR
Step 1: R_{FX} = (1.339 / 1.3)  1 = 3%
Step 2: R_{DC} = (1.05 * 1.03)  1 = 8.15%
Portfolio Currency Formula
Step 1: Calculate R_{DC} for each
Step 2: Apply the weights for each
Note: foreign currency must be the base currency
Currency Risk Formula
std^{2}_{RDC} = std^{2}_{RFC} + std^{2}_{RFX} + 2(std_{RFC} * std_{RFX} * cor)
Types of Currency Hedges
Reasons to or not to hedge
 Passive hedging: matching benchmark
 Discretionary hedging: some deviation (goal is risk reduction)
 Active hedging
Reasons to NOT hedge:
 Time and cost
 Zerosum game
Reason TO hedge:
 Extreme shortterm movements
 Inefficient pricing
What is the Currency Economic Fundamentals Approach?
Currencies increase when?
Reversion to fair value and based on PPP
Currencies increase when:
 Low inflation
 higher real/nominal rates
 undervalued
Carry Trade Approach
Borrowing in lower interest rate country and investing in higher one
 CIRP exists (high interest rate currency trades at a discount)
 UCIRP is violated
 Volatility spikes can create losses
Calculate the forward rate by: Spot * (1 + R_{D}_{C} / 1 + R_{F}_{C})
Example
S = 1.100 USD/EUR r_{USD} = 4%, r_{EUR} = 1%, calculate Forward rate
1.100/(1.04/1.01) = 1.133 USD/EUR
Active Trading Actions
Currency
Volatility
Market Conditions
Expectation Action
Relative Currency App Reduce hedge or go long
Dep Increase hedge / decrease long
Volatility Rising Long straddle, long strangle (OOM)
Falling Short straddle, short strangle (OOM)
Market conditions Stable Carry trade
Crisis Stop carry trade
Why use forward (as opposed to futures) contracts for hedging?
 Customizable
 Can be used for all currencies
 Does not require margin
 Better liquidity
Static vs Dynamic Hedging
Static: buying a hedge and leaving alone
Dynamic: buying a hedge and adjusting during duration
Approaches for a 3 month hedge
 Buy one month hedge 3 times
 creates interim cash needs
 Buy 3 month hedge and offset each month with a new hedge
 more accurate BUT costs more
 Buy 3 month hedge and leave alone
Hedged vs Unhedged Formula
Forward Premium/Discount
(Forward / Spot)  1
Spot Appreciate/Depreciate
(Forecast / Spot)  1
Example:
Spot Forward Forecast Spot Prem/Dis Spot app/depr
BRL/AUD 2.1046 2.1523 2.0355 2.27% 3.28%
BRL/CHF 2.5309 2.4641 2.5642 2.64% 1.32%
You would overhedge (hedge ratio > 1) AUD
Not hedge CHF (hedge ratio < 1)
What is Roll Yield?
How does it affect the hedge?
Return on the movement of the forward price towards the spot price
Hedge Price Curve Upward Price Curve Downward
Long Negative roll yield Positive roll yield
Short Positive roll yield Negative roll yield
Negative RY = higher costs, discourages hedging
Positive RY = lower costs, encourges hedging
Using Cap weighting Pros/Cons
Pros
 Based on objective measure
 Macro consistent
 Does not require rebalancings for splits/dividends
Cons
 Exposed to market bubbles
 Lead to overconcentration
Using Price Weighting Pros/Cons
Pros
 Easy
 Lots of price history
Cons
 Not tied to economics of company
 Splits can impact a security
 Does not relfect portfolio construction
Daily VaR Formula
(R_{annual}/days)  std_{from the mean} * (std_{annual} / √days)
Leverage and Std Using Corner Portfolios
Tangency = Highest sharpe portfolio
Std would be lowest on the levered portfolio