CFA Level 3 All Formulas, Tables, Diagrams and Problem Sets

   

Reading 6 - Overview of GIPS

 

Reading 7 – The Behav Fin Perspective

Reading 23 - Passive Eq Investing

Reading 8 – The Behav Biases of Individuals

Reading 24 - Active EQ Investing - Strategies

Reading 9 – Behav  Fin & Investment Process

Reading 25 - Active EQ Investing - Port Con

Reading 10 – CME Part 1

Reading 26Hedge Fund & Strategies

Reading 11 – CME Part 2

Reading 27 - Asset Alloc to Alternatives

Reading 12 - Overview of Asset Allocation

Reading 28 - Overview of PWM

Reading 13 - Principles of Asset Allocation

Reading 29 - Taxes and Private WM

Reading 14 - Asset Alloc w Real-Wrld Cnstrnts

Reading 30 - Estate Planning in Gbl Cntxt

Reading 15 - Option Strategies

Reading 31 - Conc Single-Asset Positions    

Reading 16 - Swaps, Fwds and Futures Strategies

Reading 32 - Risk Mgmt for Individuals

Reading 17 - Ccy Mgmt - An Intro

Reading 33 - Port Mgmt for Inst Investors

Reading 18 - Overview of FI Port Mgmt

Reading 34 - Trade Strategy and Exec

Reading 19 -  Liab-driven & Index-Based Strat

Reading 35 - Port Perf and Eval

Reading 20 - Yield Curve Strategies

Reading 36 - Investment MGR Selection

Reading 21 - FI Active Mgmt - Cr Strategies

Reading 37 - Case study in PM - Instutional

Reading 22 - Overview of Eq Port Mgmt

Reading 38 - Case Study Risk Mgmt - PWM





 

CF Weighting Factor

 

A

 

B

 

C

 

D

 

Total

Beg Assets (31 May)

 

100

97.4

112.94

124.47

434.81

External cash flows

 

 

 

 

 

 

5th June

.83

10

15

 

 

25

8th June

.73

 

 

 

-15

-15

17th June

.43

 

-5

 

 

-5

24th June

.2

 

 

 

-6.5

-6.5

29th June

.03

 

-2.5

 

-4.0

-6.5

Ending assets

(30 June)

 

 

110.55

 

105.2

 

113.3

 

100.5

 

429.55

Beginning assets + weighted cashflows

 

 

108.3

 

107.63

 

112.94

 

112.1

 

440.97

% of total beginning assets

 

 

23.0%

 

22.4%

 

25.9%

 

28.63%

 

100%

% of total beginning assets + weighted cash flows

 

 

24.56%

 

24.42%

 

25.61%

 

25.42%

 

100%


 

% of beginning assets

% of beginning assets + weighted cash flows

Return for month of June

Portfolio A

23.0%

24.56%

.51%

Portfolio B

22.4%

24.42%

.28%

Portfolio C

25.97%

25.61%

.32%

Portfolio D

28.63%

25.42%

1.36

 

100%

100%

 



Beginning assets

rc = (.0051 * .23) + (0.0028 *.224) + (.0032 * .2597) + (.0136 * .2863) = 0.0065 = .65%

Beginning assets plus weighted cash flows

r= (.0051 * .2456) + (0.0028 *.224) + (.0032 * .2561) + (.0136 * .2542) = 0.0062 = .62%




Basic axioms (basic rules) of utility theory

Completeness - Assumes that an individual has well-defined preferences and can decide between any two mutually exclusive alternatives.

Transivity - assumes that, as an individual decides according to the completeness axiom, an individual decides consistently.

Independence - also pertains to well-defined preferenes and assumes that the preference order of two choices combined in the same proportion with a third choice maintains the same perference order of the two choices. 

Continuity - assumes there are continuous (unbroken) indifference curves such that an individual is indifferent between all points, representing combinations of choices on a single indifference curve.


Bayes' Formula



P (A|B) - conditional probability of event A given B. It is updated probability of A given the new information B.

P (B|A) - conditional probability of B given A.  


Subjective Expected Utility


E(U)  - expected utility

Utility (Prospect Theory)


w = probability-weighting function for outcome x; accounts for tendency to overreact to low probability events and underreact to other events

p1 and  p2: probabilities of the outcomes
w: subjective weighting function
v: reflects a larger impact to losses than gains
x1 and x2 - potential outcomes  






Friedman-Savage Double-Inflection Utility Function

Double inflection utility function - A utility function that changes based on the levels of wealth

 


Value Function

The value function which passes through the reference point, is s-shaped; moreover , as its asymmetry implies, given the same variation in absolute value there is a bigger impact of losses than gains (loss aversion). People are not risk-averse but rather loss-averse






Reading 8  - The Behavioral Biases  of Individuals

Relative Wealth & SLR

Biases are Primarily

Adapt to or Moderate the biases of the client

Allowable Deviations Up and Down from Optimal Weight

High RW & low SLR

Emotional

Adapt to

10% to 15%

High RW & low SLR

Cognitive

Some of both

5% to 10%

Low RW & high SLR

Emotional

Some of both

5% to 10%

Low RW & high SLR

Cognitive

Moderate

0% to 5%





Reading 9  - Behavioral Fin & Investment Process





   - Aggregate value of market equity

  - level of nominal GDP







Historical equity returns − Historical 10-year government bond yield = Historical equity risk premium

Expected equity return − Current 10-year government bond yield = Expected equity risk premium

Net Exports = Net Private Savings + Govt Surplus
(X - M) = (S - I) + (T - G)


10.1 Calcuate the short-term interest rate target given the following information

Neutral Rate

4.0%

Inflation Target

2.0%

Expected Inflation

4.0%

GDP Long-Term Trend

3.0%

Expected GDP

5.0%


short-term rate =  neutral rate + expected inflation rate + .5 (GDP expected - GDP trend) + .5 (Inflation Expected - Inflation Target)

= 4% + 4% + .5 (5% - 3%) + .5 (4% - 2%) =  8% + 1% + 1% = 10%

10.2 Calcuate the short-term interest rate target given the following information

Neutral Rate

4.0%

Inflation Target

2.0%

Expected Inflation

5.0%

GDP Long-Term Trend

3.0%

Expected GDP

1.0%



short-term rate =  neutral rate + expected inflation rate + .5 (GDP expected - GDP trend) + .5 (Inflation Expected - Inflation Target)

= 4% + 2% + .5 (1% - 3%) + .5 (5% - 2%) =  4% + 5 + 1% + 1% = 9% + -1 + 1.5 = 9.5%


First impact of policy - 

 

Fiscal Policy

 

 

 

Monetary Policy

 

 

Loose

Tight

Loose

High Real Rates +

High Expected Inflation

= High Nominal Rate

Low Real Rates +

High Expected Inflation

= Mid Nominal Rate*

Tight

High Real Rates +

High expected Inflation

= Mid Nominal Rate*

Low Real Rates +

High Expected Inflation

= Low Nominal Rate



Two cases involve a mix of loose and tight policy. In these cases, the combined impact could be higher or lower nominal rates. Nominal rates are labelled as "mid" level for these cases.



Reading 11 - Capital Market Expectation, Part 2 : Forecasting Asset Class Returns


Expected Return - Discounted Cash Flow Approach



D/P  is the dividend yield, %ΔE is the expected percentage change in totaal earnings, %ΔS is the expected percentage change in shares outstanding, %ΔP/E is the percentage  change in the P/E ratio. The term in parentheses (%ΔE - %ΔS ) is the growth rate of earnings per share. Net purchases (%ΔS < 0) imply that earnings per share grows faster than total earnings 

For long time horizon 


Expected cash flow return (income return)


Expected nominal earnings growth

 

Expected Repricing Return


Dividend Yield                           = 3.2 %
Repurchase Yield                       = .75 %
Growth in Nominal GDP           = 3.2 %
Premium for corporate growth  = .97%
PE Expected to fall by               = .16


E(R) = 3.2 + 3.2  -(- .75) + .97 - .16 = 7.96%

The Grinold-Kroner model estimates the expected return on equity as flows






E(R) - expected rate of return on equity
D/P - expected dividend yirekd
i - expected inflation 
    g - expected real total earnings growth rate 

Singer-Terhaar Model




11.1 

Emerging small-cap equity - Std Dev - 23%
Global investable market (GIM) 7.00%
Correlation with GIM - .85
Degree of integration with GIM - .65

Risk-free rate: 2.5%   
Illiquidity premium: 60 bps
Sharpe ratio for GIM and emerging small-cap equity: 0.31

the forecast of the expected return for small-cap emerging market equities is closest to:

Step 1: Systematic risk premium in fully integrated market
RP = rho * sigma * sharpe ratio
      = .85 * .23 * .31
      = .0606 
      = 6.06%

Step 2: Systematic risk premium in fully segmented market
RP = sigma * sharpe ratio
      =  .23 * .31
      = .0606 
      =  7.13%

Step 3: Weight systematic risk premiums by degree of integration:

0.65 × 6.06 + 0.35 × 7.13 = 6.43%

Step 4: Add the illiquidity premium

6.43% + 0.60% = 7.03%

Step 5: Add the risk-free rate:

2.5% + 7.03% = 9.53% -> Expected Return


Historical equity risk premium

Historical equity returns - historical 10-year govt bond yield = Historical equity risk premium


Real Estate -  Expected Return

 

----------------------------------------------------------------------------------------------------------
Apartment
Cap Rate = 5%
NOI = 2%
NOI growth rate = 4%

E(R) = Cap Rate + NOI Growth Rate = 5 + 4 = 9%

Office building
Cap Rate = 4.5%
Lease payments expected to grow by = 2% (NOI Growth Rate)
Cap Rate expected to increase by .5 %

E(R) = Cap Rate + NOI Growth Rate - %change in Cap Rate = 4.5 + 2 - .5 = 6%

There is a clear pattern of high cap rates for riskier property types, lower-quality properties versus high-productivity and less attractive locations

----------------------------------------------------------------------------------------------------------

Exchange Rates

The expected change in the exchange rate will reflect the differences in the nominal short-term interest rates (r), term premiums (Term)   


Estimating Volatility

In a model with K common factors, the return of the ith asset is given by


the variance of the ith asset is






As an example, if  , then the true variance, var (r), of the asset is 9 times the variance of the observed data.


ARCH Formula


α + β is < 1. Higher value of α + β indicate higher emplasis on past information, leading volatility clustering. 





  (return in period t was 3% above expectations) 






Economic Net Worth = Economic Assets - Economic Liabilities

Asset Alloc Approach

Relation to Economic Balance Sheet

Typical Objective

Typical Uses and Asset Owner Types

Asset Only

Does not explicitly model liabilities or goals

Maximize Sharpe ratio for acceptable level of volatility

Liabilities or goals not defined and/or simplicity is important

          Some foundations, endowments

            SWF

            Individual Investors

Liability Relative

Model legal and quasi-labilities

Fund liabilities and invest excess asset for growth

Penalty for not meeting liabilities high

            Banks, Defined benefit pensions, Insurers

Goals Based

Model goals

Achieve goals with specified required probabilities of success

Individual Investors


Reading 13 - Principles of Asset Allocation



Reading 14 - Asset Alloc with Real World Constraints


  



Put-Call Parity



Put-Call-forward Parity




Greeks

Delta

    

Delta for long calls is always postieive; delta for long puts is always negative

Gamma


Gamma is a measure of the curvature in the option price in the relationship to the underlying price. Gamma for long calls and long puts is always positive


Vega


Theta









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Q 16.1 Consider an investment portfolio with $7,000,000 in govt bonds and an average modified duation 7.5. The portfolio manager wants to reduce the overall duration of the portfolio to 3.5 to hedge against an interest rate hike using 10-yr swaps with a modified duration of about 10

Answer - The should enter a pay-fixed receive floating swap. The notional amount is: 


= 7,000,000 * (3.5-7.5)/10 = USD 2,800,000

----------------------------------------------------------------------------------------------------------
Q 16.2 BPV = 89.57 | CTD Price = 97.65 | conversion factor = 0.68| contract size = 150,000




----------------------------------------------------------------------------------------------------------
Q 16.3 Assume the current three-month reference rate is 1.2% annualized. A $1,000,000 deposit is expected in one month, but interest rates are expected to drop.  How much will be receieved from the deposit and the hedge of the three-month reference rate drops to .8%

A three-month futures contract can be bought at 98.8 (100 - 1.2), locking in the forward rate of 1.2% 

------------------------------------------------------------------------------------------------------------
Futures number of contracts needed



Q 16.4 A USD 3,000,000 bond portfolio has a modified duration of 6.3. THE CTD bond has a conversion facor of .08, a bond price of 100.15, and a modified duration of 4.3. The futures contract size is USD 100,000. How many futures contracts are required to fully hedge against an interest rate rise ?

The number of contracts follows from: 

BPV (portfolio) = 3,000,000 * 6.3 * .01% = $1,890
BPV (ctd) = 100,000 * 4.3 * 100.15/100 *.01% = 43.06

# of contracts = [(BPV(T) - BPV(P))/BPV (CTD ) ] * CF = [(0 - 1890)/43.06] * .85 = -37.3

About 37 contracts should be sold to fully hedge this porfolio

----------------------------------------------------------------------------------------------------------
Q 16.5  Portfolio $60M with beta = 1.2 want to reduce beta =0.8. Beta of Futures = 1, futures price 2,984 with a $250 

# of contracts = 60 [.8 - 1.2]/(2,984 * 250) = -32.17

=> means sell 32 contracts 

Compute the effectiveness of the strategy if the S&P falls by 1.5%

Value of the portfolio in six months 

60,000,000 [1 -(.015 * 1.2)] = $58,920,000

Futures in six months 2984 (1 -.015) = 2,939
Futures profit (2,984 - 2,939) * 250 * 32 = $360,000
Net Position:  $58,920,000 + $360,000 = $59,280,000

Return (loss) = $59,280,000/60,000,000 = -1.2%



 

 

Duration Matching

Cash Flow Matching

Yield curve assumptions

Parallel YC shifts

None

Mechanism

Risk of shortfall in cashflows in minimized by matching duration and PV of liab stream

Bond portfolio CF match liabilities

Basic Principle

CF come from coupon and principal repayments of the bond portfolio and offset liability cash flows

Cashflows, coupons and principal repayments of bond portfolio offset liability CF

Rebalancing

Frequent rebalancing required

Not required but often desirable

Complexity

High

Low


Leveraged Return


Borrowed Funds = $45 mil
Equity = $125 mil

Borrowing rate      = 5
Investment Return = 6.7

Levered Return = 6.7 + 45/125 (6.7 -5) = 7.31%

Money Duration is market value multiplied by modified duration, divided by 100.

PVBP is market value multiplied by modified duration, divided by 10,000. PVBP scales money duration so that it can be interpreted as money gained or lost for each basis point change in the reference interest rate. For example, a portfolio with $10 million market value and a duration of 6 PVBP = $6000

($10 million * 6) / 10,000 = $6,000




Money duration is equal to market value x modified duration divided by 100.




Butterfly spread = -(short-term yeld) + ( 2 * medium-term yield) - long-term yield


Predicted change = Portfolio par amount * Partial PVBP * (–Curve shift)


Yield Curve Scenario

Barbell

Bullet

Level Change

Parallel shift

Outperforms

Underperforms

 

Slope Change

Flattening

Outperforms

Underperforms

Steepening

Underperforms

Outperforms

 

Curvature Change

Less Curvature

Underperforms

Outperforms

More Curvature

Outperforms

Underperforms

 

Rate volatility change

Decreased rate volatility

Underperforms

Outperforms

Increased rate volatility

Outperforms

Underperforms



Q 20. 1 What mix of 2 yr and 30 yr,  can be used to replace the 2 yr bond ?


Maturity

Coupon

Price

Yield to Maturity

Effective Duration

Effective Convexity

2 years

5.10

101.50

4.30

1.870

5.34

10 years

7.95

103.50

7.45

6.800

61.88

30 years

9.15

97.00

9.45

9.920

171.72


6.80 = (Duration of 2-year note × Weight of 2-year note) + (Duration of 30-year bond × Weight of 30-year bond)
= 1.87 x + 9.92(1 – x )
         = 38.76%.


Q 20. 2 Amount that should be allocated for 

 Maximum position that the client can take in long-term bonds is C$150 million

MaturityYTM (%)DurationPVBP (C$ millions)
2-year1.731.97197
5-year2.014.78478
10-year2.558.89889
Long-term3.1619.601,960

PVBP = 150 * 1,960 = C$294,000

2-year = 294,000/197 = C$ 1,492 million

Q 20.3 Calculate expected return 

Bullet PortfolioBarbell Portfolio
Investment horizon (years)1.01.0
Average annual coupon rate for portfolio1.86%1.84%
Average beginning bond price for portfolioC$100.00C$100.00
Average ending bond price for portfolio
(assuming rolldown and stable yield curve)
C$100.38C$100.46
Current modified duration for portfolio4.964.92
Expected effective duration for portfolio
(at the horizon)
4.124.12
Expected convexity for portfolio
(at the horizon)
14.6824.98
Expected change in government yield curve–0.55%–0.55%


Q 20.4 What is the difference in the rolling yield between bullet portfolio and barbell portfolio?

6 bps

Return ComponentFormulaBullet PortfolioBarbell Portfolio
Yield incomeAnnual coupon payment/Current bond price1.86/100.00
= 1.86%
1.84/100.00
= 1.84%
+ Rolldown return(Bond priceeh – Bond pricebh)/Bond pricebh(100.38 – 100.00)/100.00
= 0.38%
(100.46 – 100.00)/100.00
= 0.46%
= Rolling yieldYield income + Rolldown return= 2.24%= 2.30%



Q 20.4  Calculate Total Return 

Return Component

Formula

Barbell
Return (C)

Yield income

Annual coupon payment/Current bond price

1.84/100.00
= 1.84%

+ Rolldown return

(Bond priceeh – Bond pricebh)/Bond pricebh

(100.46 – 100.00)/100.00
= 0.46%

= Rolling yield

Yield income + Rolldown return

= 2.30%

+ E(change in price based on yield view)

(–MDeh × ∆yield) + [½ × Convexity × (∆yield)2]

[–4.12 × –0.55%] + [½ × 24.98 × (–0.55%)2]
= 2.30%

= Total expected return

= 4.60%























Q20.5 Based on Exhibit 1, which short position is most likely to be included in the condor outlined in Scenario  below


Construct a condor to benefit from less curvature in the 5-year to 10-year area of the yield 

curve. The condor will utilize the same 1-year, 5-year, 10-year, and 30-year bonds held in the 

Fund. The maximum allowable position in the 30-year bond in the condor is $17 million, and 

the bonds must have equal (absolute value) money duration.

To profit from a decrease in yield curve curvature, the correct condor structure will be: short 1s, long 5s, long 10s, and short 30s. The positions of the condor will be: short $338 million 1-year bond, long $71 million 5-year bond, long $38 million 10-year bond, and short $17 million 30-year bond.

This condor is structured so that it benefits from a decline in curvature, where the middle of the yield curve decreases in yield relative to the short and long ends of the yield curve.

To determine the positions, we take the maximum allowance of 30-year bonds of $17 million and determine money duration. Money duration is equal to market value x modified duration divided by 100. 30-year bond money duration = $17 million × 19.69 = $334.73 million. The market values of the other positions are:

1-year bond: $334.73 million/0.99 = $338.11 million or $338 million

5-year bond: $334.73 million/4.74 = $70.62 million or $71 million

10-year bond: $334.73 million/8.82 = $37.95 million or $38 million

Q 20.6 What is ths expected return on Buy-and-Hold portfolio ?

Buy-and-Hold Portfolio

   Ride-the-Yield Curve Portfolio

Investment horizon (years)

1.0

1.0

Bonds maturity at purchase (years)

1.0

2.0

Coupon rate

1.40%

1.75%

Yield to maturity

1.65%

1.80%

Current average portfolio bond price

A$99.75

A$99.90

Expected average bond price in one year for portfolio

A$100.00

A$100.10

Expected currency gains or losses

–0.57%

–0.57%

  

Return Component

Formula

Buy-and-Hold Portfolio

Yield income

Annual coupon payment/Current bond price

1.4/99.75
= 1.4%

+ Rolldown return

(Bond priceeh – Bond pricebh)/Bond pricebh

(100 – 99.75)/99.75
= 0.25%

= Rolling yield

Yield income + Rolldown return

= 1.65%

+ Expected currency gains or losses

 

-.57%

= Total expected return

= 1.08%


Q 20.7 What is the total expected return ?

 

Bullet

Barbell

Investment horizon (years)

1.0

1.0

Average bond price for portfolio currently

98.00

98.00

Average bond price for portfolio in one year

(assuming stable yield curve)

99.75

100.00

Expected effective duration for portfolio (at the horizon)

3.95

3.95

Expected convexity for portfolio (at the horizon)             

19.50

34.00

Expected change in government bond yield curve

–0.60%          

–0.60%


Return Component

Formula

Bullet

Barbell

Yield income

Annual coupon payment/Current bond price

0

0

Rolldown yield

Bond priceeh – Bond pricebh)/Bond pricebh

(99.75-98)/98= 1.78%

(100-98)/98=2%

Rolling yield

Yield income + Rolldown return

1.78%

2.04%

E(change in price based on yield view)

(–MDeh × ∆yield) + [½ × Convexity × (∆yield)2]

(-3.95) (-.6)+.5 (19.5) (.6)^2 =

2.37 + .035  = 2.4051%

(-3.95) (-.6)+.5 (34) (.6)^2 =

2.37 + .035  = 2.43%

Total Expected Return

 

4.1908%

 

4.4720%



Reading 21 - Fixed Income Active Management - Credit Strategies

Benchmark spread = [Yield of security with little or no credit risk (benchmark bond)] - [yield on security with a similar duration]

G-spread - spread over an actual or interpolated government bond. A benefit of the G-spread is that when the maturity of the credit security differs from that of the benchmark bond, the yields of two government bonds can be weighted so that their weighted average maturity matches the credit security’s maturity.

I-spread - interpolated spread. Spread over swap curve 

Z-spread  - or zero-volatility spread, is the yield spread that must be added to each point on the implied yield curve to make the present value of a bond's cash flows equal to its current market price

OAS = z-spread - OC



21. 1 Port Mgr observes that the 7-year Treasury note's yield has fallen from 1.53% to 1.43% while the 10-year note yield remains unchanged 

 

Price

Yield

Maturity

Effective

Duration

Citigroup 3.75% due 16 June 2024

103.64

3.24%

7.96

7

US Treasury 1.5% due 31 March 2023

99.8

1.53%

7

6.7

US Treasury 1.625% due 15 Feb 2026

98.7

1.77%

9.88

9.1



x * 7 + (1-x) 9.88 = 7.96
7x  + 9.88 - 9.88 x = 7.96 
x = (9.88 - 7.96 ) / (9.88 - 7) = 66.7%

Therefore, the lineraly interpolated yield on benchmark security

66.7 *1.53 + 33.3 * 1.77 = 1.61%

and the G-spread on the Citigroup bond is 163 bps - 3.24 - 1.61 = 1.63%


21. 2 One of the high-yiled bonds of EKN Corp, the bond has a price of 91.82, a modified duration of 8.47 and a spread duration of 8.47. Interest rate increases by 20 bps, credit spread increases by 20 bps. What is the impact on the price ?

Approx percentage change increase in interest rate by 20 bps:   (-8.47) (.2%) = 1.69 %
Approx percentage change increase in credit sprd   by 20 bps:   (-8.47) (.2%) = 1.69 % 

combined effect -3.388 or price decreases roughly by 3.4%

 


Credit

Rating

PD

Spread

Duration

Z-Spread

Expected Change

 in Z-Spread

Loss

Severity

Bond D

A

0.25%

3

0.75%

+0.25%

40%

Bond E

Baa

0.50%

3.5

1.00%

+0.25%

50%

Bond F

Ba

0.75%

4.0

1.25%

+0.25%

60%


Holding period 1 year, Bond D is preferable

Bond D

 (s × t) – (∆s × SD) – (t × p × L) =  .0075(1) - .0025 (3) – (1) (.0025) (.40)

= .75 - .75 – .1 = -.1%

Bond E

(s × t) – (∆s × SD) – (t × p × L) =  .01(1) - .0025 (3.5) – (1) (.005) (.50)

= .01 - .00875 – .0025 =-.125%

Bond F

(s × t) – (∆s × SD) – (t × p × L) =  .0125(1) - .0025 (4) – (1) (.0075) (.6)

= .0125 - .01 – .0045 = .2%


21.3  Corporate bond has a spread duration of 5 years and a credit spread of 2.75%

What is the approximate excess retun if the bond is held six months and the credit spread narrows 50 bps to 2.25%? Assume the spread duration remains at five years and that the bond does not experience default losses


21. 4 What is the instantaneous excess return if the spread rises to 3.25% ?



21. 5 The investor holding period is one year

Index Rating CategoryCurrent OAS in bpsExpected OAS in one yearExpected Credit Loss RateSpread Duration
A2441180.00%5.6
Baa3342060.04%6.1
BaaBa5710.0%4.4

Bond X has the highest expected excess return (EXR) and is calculated as follows:

EXR ≈ (s × t) – (Δs × SD) – (t × p × L),
where s is the spread at the beginning of the holding period, t is the holding period expressed in fractions of a year, and Δs is the change in the spread over the holding period.

Bond X:
EXR ≈ (0.68% × 0.25) – (–0.30% × 2.4) – (0.25 × 0.70% × 55%) = 0.79%.

Bond Y:
EXR ≈ (1.74% × 0.25) – (–0.30% × 1.4) – (0.25 × 4.3% × 60%) = 0.21%.

Bond Z:
EXR ≈ (2.63% × 0.25) – (–0.30% × 1.1) – (0.25 × 13.8% × 65%) = –1.26%.


21. 6 What characterstics are used to evaluate bond spread 

BondIssue DateMaturityIssue SizeBond StructureZ-spread
A6/30/20146/30/202420,000,000Unsecured1.45%
B3/31/20173/31/2024150,000,000Secured0.89%
C9/30/20179/30/2024100,000,000Unsecured1.23%


Bond A has a higher spread than the other bonds because of its following characteristics, which Bookman should identify and discuss. Those characteristics pertain to its issuance date, issue size, and structure.

Issuance date: Bond A has the oldest issuance date. Bonds that have not been issued recently tend to have wider bid–offer spreads and lower daily transaction volume.

Issue size: Bond A has the smallest issue size. Bonds with smaller issue sizes may be less frequently traded and held by a smaller number of market participants, indicating the bonds may be less liquid. Relatively illiquid bonds often carry greater spreads to compensate investors for this disadvantage.

Bond structure: Bond A is unsecured with a lower priority in the capital structure, unlike Bond B. Subordinated debt normally offers greater credit spreads than senior debt.

CDO Structure

Senior

The safest and first one to receive the payouts. But, have the lowest interest rate

 

Mezz

moderate risk, and a bit higher interest rate

Mezzanine tranche of a CDO increases by more than the senior tranche whenever correlations increase.

Equity

Most risky and offers the highest interest rate. The payouts are made after all payouts are made for super senior and mezzanine tranches

As correlations increase, the values of the equity tranches usually increase relative to the values of the senior and mezzanine tranches.



Reading 22 - Overview of Eq Port Mgmt



Reading 23 - Passive Equity Investing




 

Fundamental

Quantitative

Style

Subjective

Objective

Decision-making process

Discretionary

Systematic, non-discretionary

Primary resources

Human skill, experience, judgement

Expertise in statistical modelling

Information Used

Research (company/Industry/economy)

Data & statistics

Analysis focus

Conviction (high depth) in stock , sector, region-based selection

A selection of variables, subsequently applied broadly over a large number of securities

Orientation of data

Forecast future corporate parameters and establish views on companies

Attempt to draw conclusion from a variety of historical data

Port Construction

Use judgement and conviction within permissible risk parameters

Use optimizers


Company

Price

12-Month Fwd EPS

3-year EPS Growth Forecast

Dividend Yield

Industry Sector

Sector Avg P/E

A

50

5

20%

1%

Industrial

10

B

56

2

2%

0%

Info. Tech

35

C

22

10

-5%

2%

Consumer Staples

15

D

32

2

2%

8%

Utilities

- 16

- Company A's forward P/E is 50/5 = 10, and its P/E -to-growth  ratio is 10/20 = .5

Company B's forward P/E is 56/2 = 28, and its P/E -to-growth  ratio is 28/2 = 14.  P/E is lower than average sector P/E this is a good candidate for relative value approach. 

- Company C is negative P/E and D is 16/2 = 8

Company A has favorable valuation relative to growth, 


Examples of Investment Styles

Characteristics based

Value, Growth or Blend/Core

Capitalization

Volatility

Membership based

Sector

Country

Market (developed or emerging)

Positions based

Long/short (net long, shot or neutral)


Returns-Based Style Analysis






Reading 25 - Active EQ Investing - Port Con







Reading 26 - Hedge Fund & Strategies


Equity

Event Driven

Relative Value

Opportunistic

Specialist

Multi-Manager

Long/Short Equity

Dedicated Short Bias

Equity Market Neutral

Merger Arb

Distressed Securities

Fixed Income Arb

Convertible Bond Arb

Global Macro

Managed Futures

Vol Strategies

Reinsurance Strategies

Multi-strategy

FoF


Conditional Risk Factor Model




Reading 27 - Asset Alloc to Alternatives

 


The NAV of an investor's share in a private renewable energy fund is $30 million at the end of 2020. All capital has been called. The investor expects a 20% distribution to be paid at the end of 2021. The expected growth rate is 12%. What is the expected NAV at year-end 2022 ?


 

 = $30,105,600



Reading 28 - Overview of PWM




Returns-based Taxes: Accural taxes on interest and dividends


Amount = 100, r = 7%, n = 20, and t = 20%



Without taxes, FV = 387. Difference = 90

Tax Impact = 90/287  = 31% which is greater than > 20%


Returns-based Taxes: deferred captial gains


 

Scenario 1

Amount = 100, cost basis = 100, r = 7%, n = 20, and t = 20%


Deferring taxes is better than getting taxed every year

Scenario 2

Amount = 100, cost basis = 80, r = 7%, n = 20, and t = 20%


Wealth-based Taxes



P = 500,000 | wealth tax = .5% | r = 5% | n = 20


Annual return after realized return (r*)






What is the expected future accumulation in 15 years assuming these parameters hold for that time period?

Hypothetical Tax Profile and Example
Tax ProfileAnnual Distribution Rate (p)Tax Rate (T)
Interest (i)20%35%
Dividends (d)30%15%
Capital gain (cg)40%25%

expected return is 6%



 

If cost basis = 700,000 then B = 700,000/1,000,000 = 0.7



Tax-Deferred Accumulation


P = 10,000 | r = 7.5% | n = 15 | Tn = 20%




Reading 30 - Estate Planning in a Global Context


Taxable Estate                              Tax Rate
upto 600,000                                        2
60,001         - 1,500,000                       4
1,500,001    - 3,000,000                       7
3,000,000    - 4,500,000                      11
4,500,000    - 6,000,000                     15
6,000,001    - 10,000,000                   20
10,000,001   - 15,000,000                  26
15,000,001   - 40,000,000                  33
40,000,001   - 100,000,000                41
Over 100,00,000                                 50

Taxable Estate 2,000,000

upto 600,000 (2%)                             12,000
tax on next 900,000 (4%)               =     36,000
tax on remaining 500,000 (7%)      =     35,000
-----------------------------------------------------------
Estate estate tax                                            83,000
------------------------------------------------------------

 




Reading 31 - Conc. Single Asset Positions





P(s) - probability of surviving to a given year
w(t-1) - wage in the prior period
g - annual wage growth rate
r - nominal risk free rate
y - risk adjustment


32.1 

Wage growth rate = 2%
Risk-free rate = 4%
Income vol = 3%
Total disc rate = 7%

Year Rate of return

Wages (2% annual growth)

Present value od wages

Probability of Survival

Probability weighted wages

1

51,000

47,664

99%

47,187

2

52,020

45,436

98%

44,527

3

53,060

43,313

98%

42,447

4

54,122

41.289

97%

40,050

5

55,204

39,360

96%

37,786

Total

 

 

 

$211,997


Economic (Holistic) Balance Sheet


Assets

Liabilities

Financial Capital

 

Debt

 

  Liquid Assets

$275,000

 Credit card debt

15,000

  Investment assets

1,265,000

 Car loan

35,000

Personal Property

2,150,000

 Home mortgage

685,000

Subtotal

$3,690,000

 Home equity load

60,000

Human Capital

1,800,000

Subtotal

$795,000

Pension value

250,000

Lifetime consumption needs bequest

300,000

Total assets

$5,740,000

Total Liabilities

$4,595,000

 

 

Net Wealth

$1,145,000


1. Net payment cost Index

1. Compute the FV of the premium paid, an annunity due 

PMT = $6,500, n = 15, i = 5%, PV =0 , FV = 147,273.6 (begin mode)

2. Compute the FV of future value of dividends

PMT = $850, n = 15, i = 5%, PV =0 , FV = 19,341 (end mode)

3. Insurance cost

147,273.6 - 19,258 = 128,931.82

4. Annual payment for 15 years insurance

FV = 128,014, n = 15, i = 5%, PV =0 , PMT = 5,690.5 (begin mode)

5. Net payment cost of Index = 5,690.5/650 = $ 8.8 cost per thousand per year

2. Net payment cost Index

Face value of the whoel life policy: $100,000
Number of annual periods: 20
interest = 5%
Annual premium of $2,000 paid at the beginning of the year
Policy dividends: $500, paid at the end of the year
Cash value: $22,500 projected for the year 20

N= 20,  i = 5%, PMT = 2,000, PV = 0,   FV = ? ( mode begin)  FV = 69,439

N= 20, i =5, PMT = 500, PV = 0, FV = ? (mode end) FV = 16,533

Net Insurance cost = 52,906

N = 20, i = 5, FV = 52,906 PMT = ? (mode begin)  PMT = 1,524

Divide by US thousand of face value = 1524/100 = 15.24

3. Surrender cost Index Calculation

Net surrender cost = 52,906 - 22,500 = 30,406

N = 20, i = 5, FV = 30,406 PMT = ? (mode begin)  PMT = 877.2 per thousand = $8.76

Surrender cost index indicates the annual cost of accumulating cash during the assumed holding period. Companies with lower index value are more efficient at delivering surrender value.


Net Payment Cost Index Calc

Future value of premiums (annuity due): US$,2000 annual payment, 20 years, 5%

69,439

Future value of dividends (ordinary annuity): US$ 500 annual payment, 20 years,

16,533

20-year insurance cost

52,906

Annual payment for 20-year insurance cost (annuity due): 20 years, 5%                                  

1524

Divide by US thousands of face value

100

Net Payment Cost Index, cost per US $thousand per year

US $15.24

 

Surrender Cost Index Calc

Future value of premiums (annuity due): US$,2000 annual payment, 20 years, 5%

69,439

Future value of dividends (ordinary annuity): US$ 500 annual payment, 20 years,

-16,533

20-year cash value (given)

-22,500

20-year insurance cost

30,406

Annual payment for 20-year insurance cost (annuity due): 20 years, 5%                                  

876

Divide by US thousands of face value

100

Net Payment Cost Index, cost per US $thousand per year

US $8.76


Risk Management Techniques

Loss Characteristics

High Frequency

Low Frequency

High severity

Risk Avoidance

Risk Transfer

Low severity

Risk Reduction

Risk Retention


Calculate Insurance - Human Life Value Method

1. Adjust actual pre-tax compensation for income tax (tax rate 30%)
     $100,000 - $30,000 = $70,000
2. Adjust for family expense that will not exist after his death 
     $70,000 - $20,000 = 50,000
3.  Add the value of any non-taxable employee benefits that the family will no longer
       50,000 + 15,000 = 65,000
4. Estimate the amount of pre-tax income needed to replace that income on an aftertax
basis (tax rate 20%): $65,000/(1 – t) = $65,000/(1 – 0.20) = $81,250.
5.  Apply growth for 20 years at growth rate = 3%
6.  Discount rate = 5%
7.  (1+d)/(1+g) - 1 = 1.94%, n = 20, PMT = 81,250 , FV (annunity due) = 1,362,023





Investment Approach

Description

Norway Model

Traditional style characterized by 60%/40% equity/fixed-income allocation, few alternatives, largely passive investments, tight tracking error limits, and benchmark as a starting position

 Pros: Low cost, transparent, suitable for large scale, easy for board to understand

Cons: Limited value-added potential

Endowment Model

Characterized by high alternatives exposure, active management and outsourcing

 Pros: High value-added potential

Cons: Expensive and difficult to implement for most sovereign wealth funds and because of their large asset sizes

Canada Model

Characterized by high alternatives exposure, active management and insourcing

 Pros: High value-added potential and development of internal capabilities

Cons: Potentially expensive and difficult to manage

LDI Model

Characterized by focus on hedging liabilities and interest rate risk including via duration matched, fixed income exposure. A growth component in the return-generating portfolio is also typical.

 Pros: Explicit recognition of liabilities as part of the investment process

Cons:Certain risks (e.g longevity risk, inflation risk) may not be hedged



Factors Affecting Calculation of Defined Benefit Liabilities

Factor

Impact on Liabilities

Service/Tenure

Depending on plan design, often the longer the service or tenure, the larger the benefit payments

Salary/earnings

The faster salaries or earnings grow, the larger the benefit payment

Additional or matching contributions

Additional or matching contributions are often rewarded by a step change increase in benefit payments

Mortality/Longevity assumptions

If life expectancy increases, the obligations or liabilities will increases

Expected Vesting

If the employment turnover decreases, expected vesting will increase

Expected Investment Returns

In some cases, increases in expected returns will result in a higher discount rate – hence, lower obligations or liabilities

Discount Rate

A higher (lower) discount rate results in lower (higher) liabilities



Funded ratio =  Fair value of plan assets/PV of Defined benefit obligations





33.1 Calculate the modified duration of equity

Equity cap ratio = 9%, Mod Duration Assets = 2, Liabilities = 1.5, Δi/Δy = 85/100

A/E =  1/.09 = 11.11

a. Dur of Equity =  11.11 (2) - 10.11 (1.5) .85 = 9.33

b. what would be the impact to the value of shareholder capital of a 50bps rise in the level of yields 

.5% * (-9.33) = 4.67% => the change in the equity capitalization value 



33.2 Calculate std deviaton of equity 

Std dev Assets = 4.4% | Std Dev Lib = 3.8% | rho = .55 | A/E = 5 
Std dev Equity = (5)^2 (4.4)^2 + 3^2 (3.8)^2 - 2 (4) (3) .55 (4.4) (3.8) = sqrt (393.3) = 18.63

33.3 Calculate std deviation of equity 

Std Dev Assets = 7.0% | Std Dev Lib = 4.0% | rho = .35 | A/E = 4 
Std dev Equity = (4)^2 (7)^2 + 3^2 (4)^2 - 2 (4) (3) .35 (7) (4) = sqrt (692.8) = 26.32

33.4 Calculate std deviation of equity 

Std Dev Assets = 7.0% | Std Dev Lib = 4.0% | rho = .65 | A/E = 4 
Std dev Equity = (4)^2 (7)^2 + 3^2 (4)^2 - 2 (4) (3) .65 (7) (4) = sqrt (491.2) = 26.32


Reading 34 - Trade Strategy and Execution

Implementation shortfall metric is the most important ex post trade cost measurement used in finance. The IS metric provides protfolio manager with the total cost associated with implementing the investment decision. 



The paper return shows the hypothetical return that the fund would have received if the manager were able to transact all shares at the desired decision price and without any associated costs or fees


The actual 



IS can also be decomposed using execution cost and opportunity cost and fees




Trade Strategy and Execution







Arrival cost = side * (Avg Price - Arrival Price)/Arrival Price * 10^4 
                     = (-1) (29.5 -30)/30 * 10^4 = 166.7 bps

Index Cost = side (Index VWAP - Index Arrival Price)/Index Arrival Price * 10^4 
             = (-) (495-500)/500 * 10^4 = 100 bps

Market Adjusted Cost = Arrival Cost - beta * Index Cost
                                    = (166.7 - 1.26 * 100) = 41.7 bps

31.2                                       

Average Execution Price = $30.5
Arrival Price = $30.0

Index Arrival Price $500
Index VWAP = $505
Beta = 1.1

Arrival Cost = (Av Exec Price - Arrival Price)/Arrival Price * 10^4 = (30.5-30)/30 * 10^4
                      = 166.7 bps

Index Cost = (Index VWAP - Index Arrival Price)/Index Arrival Price = (505-500)/500 *   10^4
                    = 99

Market Adjusted Cost = Arrival Cost - beta * Index Cost = 166.7 - 1 * 99 = 67.7 bps




Equity Return Attribution - The Brinson Model


Allocation effect  



Total Allocation Effect


Selection Effect


Interaction Effect 


Carhart Model


RMRF - the return on a value weighted equity index in excess of the one month T-bill rate

SMB - small minus big, a size (market-cap) factor (SMB) is the average of the three small-cap port minus the average return on the large-cap portfolios

HML - high minus low, a value factor 
 
WML - winners minus losers, a momentum factor

E - an error term that represents the portion of the return to the porfolio, p, no explanined by the model

Factor-model-based 



Sortino Ratio


Sortino ratio = (portfolio return – target return) / target semi standard deviation
                     = (9% - 5%) / 4.12% 
                     = 0.97

YearRate of ReturnTarget rate min(rt – rT,0)^2
16%0
2-2%.0049
39%0
48%0
5-1%.0036
Total.0085


Upside Capture (UC) = 5.12% / 6.05% = 85%
Downside Capture (DC) = -0.70% / -1.14% = 61%
Capture Ratio = 85 / 61 = 1.39

The capture ratio greater than 1 indicates positive asymmetry, or a convex return profile






Manager selection Process Overview

Key Aspects

Key Question

Universe

Defining the universe

 

What is the feasible set of managers that fit the portfolio need ?

Suitability

Which managers are suitable for the IPS ?

Style

Which has the appropriate style?

Active vs. Passive

Which fit the active versus passive decision ?

Quantitative Analysis

Investment due diligence

 

Which manager “best” fits the portfolio need ?

Quantitative

What has been the manager’s return distribution?

Attribution and Appraisal

Has the manager displayed skill ?

Capture Ratio

How does the manager perform in “up” markets vs “down” markets “ ?

Drawdown

Does the return distribution exhibit large drawdowns ?

Qualitative Analysis

 

Investmen due diligence

Which manager best fits the portfolio need ?

Qualitative

Is the manager expected to continue to generate this return distribution  ?

-          Philosophy

What market inefficiency does the manager seek to exploit ?

-          Process

Is the investment process capable of exploiting this inefficiency ?

-          People

Do the investment personnel possess the expertise and experience necessary to effectively implement the investment process ?

-          Portfolio

Is portfolio construction consistent with the stated investment philosophy and process ?

Operational due diligence

Is the manager’s track accurate and does it fully reflect risks ?

-          Process & procedure

Is the back office strong, safeguarding assets and able to issue accurate reports in a timely manner ?

-          Firm

Is the firm profitable, with a healthy culture, and likey to remain in business? Is the firm committed to delivering performance over gathering assets ?

-          Investment Vech

Is the vehicle suitable for the portfolio need ?

-          Terms

Are the terms acceptable and appropriate for the strategy and vehicle ?


Type I and Type II Errors in Manager Selection

Null Hypothesis is there us no value added by the PM

 

Realization

Below expectations (no skill)

At or above expectations (skill)

Hire/Retain

Type I

Correct

Not Hire/Fire

Correct

Type II


Active Share 


Active Share vs. Tracking Risk

 

 

Active Share

Low

High

Tracking risk

High

Sector rotation

Conc. Stock pickers

Low

Closet indexer

Diversified stock pickers