CFA Level 3

Question 1

The formula for taxes levied and paid on an annual basis.

Answer 1

FV = Cost Basis x [1 + r(1 – ti)]ⁿ

ti = Interest Tax Rate

Question 2

The formula for capital gains taxes deferred until realized.

Answer 2

FV = Cost Basis x [(1 + r)ⁿ(1 – tcg) + tcg] 

tcg = Capital Gains Tax Rate

Question 3

What is the formula for the FV of an investment when the market value and cost basis are different?

Answer 3

FV = MV x [(1 + r)ⁿ(1 – tcg) + tcg(CB/MV)]  

tcg = Capital Gains Tax Rate

CB = Cost Basis

MV = Market Value

Question 4

What is the formula for a wealth based tax?

Answer 4

FV = Cost Basis x [(1 + r)(1 – tw)]ⁿ  

tw = Wealth Tax Rate

Question 5

How do you calculate the annual return after realized taxes? (r*)

Answer 5

r* = r(1 – piti – pdtd – pcgtcg)

pi = % of return attributable to interest
ti = Interest Tax Rate

pd = % of return attributable to dividends
td = Dividend Tax Rate

pcg = % of return attributable to capital gains
tcg = Capital Gains Tax Rate

Question 6

What is the formula for tax obligations from gains not yet realized in a portfolio? (T*)

Answer 6

T* = tcg(1 – pi – pd – pcg)/(1 – piti – pdtd – pcgtcg)

tcg = Capital Gains Tax Rate

pi = % of return attributable to interest
pd = % of return attributable to dividends
pcg = % of return attributable to capital gains

ti = Interest tax rate
td = dividends tax rate
tcg = capital gains tax rate

Question 7

What is the formula for the future after-tax accumulation for each unit of currency in a taxable portfolio? In this scenario, you have to adjust for future capital gains taxes.

Answer 7

FV = MV x [(1 + r*)ⁿ(1 – T*) + T* – (1 – B)tcg]  

r\* = annual realized return after taxes
T\* = tax obligations from gains not yet realized

If the cost basis is equal to market value then B = 1

Question 8

What is the formula for calculating accrual equivalent returns?

Answer 8

MV(1 + R_AE)ⁿ = FV

R_AE = Accrual equivalent return

Question 9

What is the formula for calculating accrual equivalent tax rates?

Answer 9

r(1 – T_AE) = R_AE

R_AE = Accrual Equivalent Return
T_AE = Accrual Equivalent Tax Rate

Question 10

What is a benefit of tax loss harvesting?

Answer 10

Realizing a loss saves taxes in the current year and means that the tax savings can be reinvested. This technique increases the amount of capital the investor can put to use.

Question 11

What three assumptions does traditional finance make about investors?

Answer 11

1. They are risk averse
2. They have rational expectations
3. They practice asset integration

Question 12

What three assumptions does behavioural finance make about investors?

Answer 12

1. They exhibit loss aversion
2. They hold biased expectations
3. The practice asset segregation

Question 13

Describe Methodical investors

Answer 13

1. More risk averse
2. Decisions based primarily on thinking

Question 14

Describe Individualist investors

Answer 14

1. Less risk averse
2. Decisions based primarily on thinking

Question 15

Describe Cautious investors

Answer 15

1. More risk averse
2. Decisions based primarily on feeling

Question 16

Describe Spontaneous investors

Answer 16

1. Less risk averse
2. Decisions based primarily on feeling

Question 17

What three questions do you need to consider when assessing an investors ability to take risk?

Answer 17

1. What are the investor’s financial needs and goals, both short term and long term?
2. How important are these goals? How serious are the consequences if they are not met?
3. How large an investment shortfall can the investor’s portfolio bear before jeopardizing its ability to meet major short term and long term goals?

Question 18

What should investors and managers know about a particular Monte Carlo product in order to be confident that it provides reliable information?

Answer 18

1. Any user of Monte Carlo should be wary of a simulation tool that relies only on historical data.
2. It should simulate the performance of specific investments, not just asset classes.
3. It must take into account tax consequences.

Question 19

What are the 5 investment constraints of an IPS?

Answer 19

1. Liquidity
2. Time Horizon
3. Taxes
4. Legal and Regulatory Environment
5. Unique Circumstances

Question 20

When calculating total liquid reserves are current cash equivalents included?

Answer 20

Yes.

Net proceeds from sale of shares + Cash equivalents = total liquid reserves

Question 21

How can investments provide tax deferral benefits?

Answer 21

• Investments that are not taxed until sold provide a tax deferral benefit.
• If dividend taxes are higher than capital gain taxes then NOT paying dividends is a form of tax deferral benefits.

Question 22

What is the formula for calculating the tax rate on foreign income when the deduction method is used?

Answer 22

T_{Deduction Method} = T_Residence + T_Source − (T_Residence × T_Source)

Question 23

What is financial capital?

Answer 23

Financial capital includes the tangible and intangible assets (outside of human capital) owned by an individual or household. Financial capital would include the vested portion but not the unvested portion of an employer pension plan.

Question 24

Define Human Capital

Answer 24

Human capital is the net present value of the individual’s future expected labor income weighted by the probability of surviving to each future age.

Question 25

Richard is 55 years old and would like to retire in 5 years. He has saved $200,000 in a taxable investment account and plants to contribute $10,000 to it at the end of each year for the next 5 years. He will receipe a lump-sum bonus payment of $50,000 before tax when he retires. The bonus will be taxed at 20%. If he is able to accumulate $350,000 in his investm ent account he will be able to retire comfortably. State the return objective for Richard's investment account.

Answer 25

The return objective for Richard's investment account is to see the plan, _including annual contributions of $10,000_ and a _one-time payment of $40,000 in five years' time_ grow to a nominal value of $350,000 in five years when he is ready to retire.

Question 26

When does a portfolio have liquidity constraints?

Answer 26

Only when withdrawals are needed to fund expenses. If the portfolio is being funded on an annual basis with no need of withdrawals _the plan itself has no liquidity constraints._

Question 27

Frank and Alice would like to maintain annual spending of $75,000 on an inflation-adjusted basis. Inflation is assumed to be 2%. Referencing the attachment, calculate the capitzalized value of their core capital spending needs over the next three years.

Answer 27

Capitalized value = 72,206 + 70,271 + 68,230 = 210,777

Question 28

Identify the risk of outliving one's assets and an investment product that addresses this risk.

Answer 28

Longevity Risk. Life annuities, either fixed or variable, are products that address longevity risk.

Question 29

Explain what a leveraged recapitalization is.

Answer 29

A leveraged recapitalization is essentially a leveraging of a company’s balance sheet, usually accomplished by working with a private equity firm. The private equity firm generally invests equity and provides or arranges debt with senior and mezzanine (subordinated) lenders. The owner transfers a portion of her stock for cash and retains a minority ownership interest in the freshly capitalized entity. Doing so allows the owner to monetize a large portion of her business equity (typically 60–80%) and retain significant upside potential (20–40%) from that point forward. Because of the retained stake, the owner should remain highly motivated to grow the business.

Question 30

Explain what a divesture is.

Answer 30

If a business owner is not yet ready to retire and wishes to continue to run the business but would like to generate some liquidity now in order to diversify, the owner may wish to sell or dispose of non-core assets. Non-core assets can be broadly defined as those that are not essential to the continued operation or growth of the company.

Question 31

What is one of the key beneifts of a personal line of credit secured by a company?

Answer 31

One of the key benefits is that this type of borrowing should not cause an immediate taxable event to the company or the owner if structured properly. This technique basically uses corporate debt capacity (assuming it is available) to avoid a taxable stock sale or dividend. The transaction is usually structured with a “put” arrangement back to the company to make the lender comfortable. The company can support this put obligation either through its existing credit arrangement or with a standby letter of credit issued for this specific purpose. The exercise of the put to the company as a source of repayment of the loan would likely be considered a taxable event to the business owner. Also, at some point the debt will need to be repaid.

Question 32

What are the acronyms for cognitive biases?

Answer 32

* *R**epresentativeness * *I**llusion of Control * *C**onservatism * *C**onfirmation * *H**indsight * *F**raming * *A**vailability * *M**ental Accounting * *A**nchoring and Adjustment

Question 33

What is the acronym for emotional

Question 34

What is the acronym for emiotional biases?

Answer 34

* *L**oss-Aversion * *O**verconfidence * *S**tatus Quo * *S**elf-Control * *E**ndownment * *R**egret Aversion

Question 35

Describe Loss Aversion

Answer 35

Loss Aversion is an emotional bias where investors hold their losers even if an investment has little or no chance of going buck up. Similarily, they lock in profits too soon, thus limiting their upside.

Question 36

What are the consequences of loss aversion?

Answer 36

* Hold investments in a loss position longer than justified by fundamental analysis * Sell investments in a gain position earlier than justified by fundamental analysis * Limit the upside potential of a portfolio by selling winners and holding losers * Trade excessively as a result of selling winners * Hold riskier portfolios than is acceptable. This is caused by the sale of investments that are winners and the retention of investments that are losers. FMPs may accept more risk in their portfolios than they would if they had based their decision on risk/return objectives and fundamental analysis.

Question 37

Describe Overconfidence Bias

Answer 37

Overconfidence is an emotional biases in which people demonstrate unwarranted faith in their own intuitive reasoning, judgements, and cognitive abilities.

Question 38

What are the consequences of overconfidence bias?

Answer 38

As a result of overconfidence bias, FMPS may do the following: * Underestimate risk and overestimate expected returns * Hold poorly diversified portfolios * Trade excessively * Experience lower returns than those of the market

Question 39

Describe Self-Control Bias

Question 40

What are the three specific roles of fixed-income securities in a portfolio?

Answer 40

1. Diversification benefits 2. Regular cash flows 3. Inflation heding potential

Question 41

Why do inflation-linked bonds typically exhibit lower return volatility than conventional bonds and equities?

Answer 41

Because the volatility of the returns on inflation-linked bonds depends on the volatility of **real**, rather than **nominal**, interest rates.

Question 42

Describe a fixed-coupon bond's exposure to inflation.

Answer 42

Coupon: Inflation unprotected Principal: Inflation unprotected

Question 43

Describe a floating-coupon bond's exposure to inflation.

Answer 43

Coupon: Inflation protected Principal: Inflation unprotected

Question 44

Describe an inflation-linked bond's exposure to inflation.

Answer 44

Coupon: Inflation protected Principal: Inflation protected

Question 45

What are the two conditions that need to be satisfied for achieving immunization with a duration matching fixed-income mandate?

Answer 45

1. A bond portfolio's duration must equal the duration of the liability portfolio 2. The PV of the bond portfolio's assets must equal the PV of the liabilities at *current* interest rate levels The idea is that changes in the bond portfolio’s market value closely match changes in the liability portfolio, whether interest rates rise or fall.

Question 46

What are the key features of liability-based fixed income mandates? (Duration matching and cashlow matching) * Yield curve assumptions * Basic principle * Rebalancing * Complexity

Answer 46

See attached breakdown:

Question 47

What is contingent immunization?

Answer 47

Contingent immunization combines immunization with an active management approach **when the asset porfolio's value exceeds the pv of the portfolio liability**.

Question 48

What is horizon matching?

Answer 48

Horizon matching comines cash flow duration matching approaches. Liabilities are categorized as short-term and long-term liabilities. The short-term liability (up to five year) is covered by a cash flow matching approach and long term liabilities are covered by a duration matching approach.

Question 49

Describe a model for fixed-income returns

Answer 49

See attached formula. The expected change in price is calculated as follows: [-MD x ΔYield) + (.5 x Convexity x ΔYield²)

Question 50

How do you calculated a fixed-income investment's expected change in price?

Answer 50

E(Change in price) = [-MD x ΔYield) + (.5 x Convexity x ΔYield²)

Question 51

How do you calculated a leveraged fixed-income portforlio return?

Answer 51

r_p = r_i + ((V_B/V_E) x (r_i - r_b))

Question 52

What is a type 1 liability?

Answer 52

* Known: Amount of cash outlay * Known: Timing

Question 53

What is a type II liability?

Answer 53

Known: Amount of cash outlay Uncertain: Timing

Question 54

What is a type III liability?

Answer 54

Uncertain: Amount of cash outlay Known: Timing

Question 55

What is a type IV liability?

Answer 55

Uncertain: Amount of cash outlay Uncertain: Timing

Question 56

Changes in the yield curve can be distilled into what three movements?

Answer 56

1. Level (Parallel) 2. Slope (Flattening or Steepening) 3. Curvature

Question 57

What is the formula for the butterfly spread?

Answer 57

Butterfly spread = -(Short term yield) + (2 x Medium term yields) - (Long term yield)

Question 58

What are the 4 active bond strategies under the assumption of a stable yield curve?

Answer 58

1. Buy and Hold 2. Roll down/riding the yield curve 3. Sell convexity 4. The carry trade

Question 59

What are the 3 active strategies for yield curve movement of level, slope, and curvature?

Answer 59

1. Duration management 2. Buy convexity 3. Bullet and barbell structures

Question 60

What two conditions need to hold in order to ride the yield curve?

Answer 60

1. The yield curve must be upward sloping 2. The manager must buy a bond with longer than desired maturities.

Question 61

What two stragies can be used to sell convexity?

Answer 61

1. Sell calls on bonds held in the portfolio 2. Sell puts on bonds the manager would be willing to own if, in fact, the put was exercised. Keep in mind - convexity only benefits a bondholder if there is volatility in the market. ie. Bond prices are changing.

Question 62

In what two scenarios is duration managment used for fixed income portfolios?

Answer 62

1. Duration management shortens duration in anticipation of rising interest rates 2. Lengthens duration in anticipation of falling interest rates.

Question 63

Describe a bullet portfolio and when it is used

Answer 63

A bullet portfolio targets a single segment of the curve. It is typically used to take advantage of a steepening yield curve.

Question 64

Describe a barbell portfolio and when it is used

Answer 64

A barbell portfolio combines securities concentrated in short and long maturities, relative to the benchmark. It is typically used to take advantage of a flattening yield curve.

Question 65

What are the 3 basic ways to impelement a carry trade to exploit a stable, upward sloping yield with bonds?

Answer 65

1. Buy a bond and finance it in the repo market. 2. Receive fixed and pay floating on an interest rate swap. 3. Take a long position in a bond (or note) futures contract.

Question 66

Describe the relative performance of bullets and barbells under different yield curve scenarios.

Answer 66

See attached.

Question 67

What is the formula for the Cobb-Douglas production function?

Answer 67

% Growth in GDP = % Growth in TFP + (Elasticity of Capital)(% Growth in Capital) + (Elasticity of Labor)(% Growth in Labor)

Question 68

What is the formula for the Cyclically Adjusted P/E Ratio (CAPE)

Answer 68

Current Cape = Equity Price Index (Real) / 10-Year Average Earnings (Real)

Question 69

Distinguish between a positive and negative output gap

Answer 69

A positive output gap means growth is above the trend rate and is inflationary. A negative output gap means an economic downturn with unemployment.

Question 70

Explain the permanent income hypothesis.

Answer 70

This hypothesis asserts that consumers' spending behavior is largely determined by their long-run income expectations. Consequently, short-term economic fluctuations are less likely to affect consumer spending.

Question 71

What is the Grinold-Kroner formula for expected return on equities?

Answer 71

R = Expected nominal earnings growth + Expected repricing return + expected income return Expected nominal earings growth = **Expected** Inflation + **Real** Total Earnings Growth Rate Expected Repricing Return = Change in PE Multiple Expected Income Return = **Expected** Dividend Yield - Change in Shares Outstanding

Question 72

What is the Taylor Rule?

Answer 72

R_Optimal = R_Neutral + [.5x(GDP_Forecast - GDP_Trend) + .5x(I_Forecast - I_Trend)]

Question 73

How do you calculate the required return of a bond using the risk premium approach?

Answer 73

E(Rb) = Real risk-free interest rate + Inflation premium + Default risk premium + Illiquidity premium + Maturity premium + Tax premium

Question 74

How do you calculate the sharpe ratio?

Answer 74

Sharpe Ratio = (Expected Return - RF Return) / Standard Deviation

Question 75

What is the formula for Tobin's Q

Answer 75

Tobin's Q = (MV Equity + MV Debt) / Replacement Cost of Assets

Question 76

What is the formula for Equity Q?

Answer 76

MV of Equity / (Replacement Cost of Assets - Market Value of Debt)

Question 77

What is the primary source of income for equity portfolios?

Answer 77

Dividends. Taxation is an important consideration for this type of income.

Question 78

What are three secondary sources of income for equity portfolios?

Answer 78

1. **Securitized lending**, a form of collateralized lending, may be used to generate income for portfolios. 2. **Dividend capture** is a strategy where stocks are purchased just before their ex-dividend dates to receive their dividend and then sold immediately after. 3. **Writing options**.

Question 79

Describe a high-water market in the context of portfolio management and its purpose.

Answer 79

A high-water mark is the highest value, net of fees, that the fund has reached and this protects investors from paying twice for the same performance.

Question 80

What are the two key characteristics of a tactical asset allocation? SS 10

Answer 80

1. It is short term only 2. It is an asset-only approach

Question 81

What three approaches can be used to measure the success of a tactical asset allocation (TAA)? SS 10

Answer 81

1. Sharpe Ratio 2. Evaluating the Information Ratio of the average excess of return 3. Plotting the realized return of the TAA against other porfolio's efficient frontier.

Question 82

What are the two ways that taxes impact a portfolio's return? SS 10

Answer 82

1. Lowers the mean return 2. Lowers volatility of return

Question 83

What are the 3 characteristics of a bond portfolio designed to immunize a single liablity? SS 11

Answer 83

1. Has an initial market value that equals or exceeds the pv of the liability 2. Has a portfolio Macaulay duration that matches the liability's due date 3. Minimizes the portfolio convexity statistic

Question 84

What are the 4 approaches for managing multiple liabilities? SS 11

Answer 84

1. Cash flow matching 2. Duration matching 3. Derivatives overlay 4. Contingent immunization

Question 85

What are laddered portfolios desirable for liquidity management? SS 10

Answer 85

Because there is always a bond close to redemption, the soon-to-mature bond can provide emergency liquidity needs. Barbell portfolios have maturities only at the short-term and long-term and thus are much less desirable for liquidity management.

Question 86

How do you calculate the number of futures contracts needed to fully remove the duration gap between asset and liability portfolios? SS 10

Answer 86

N_f = (BPV_L − BPV_A)/BPV_f

Question 87

Why are value-weighted bond indexes more susceptible to credit quality deterioration? SS 10

Answer 87

Compared with other weighting schemes, such as equally weighted, value-weighted indexes are tilted toward issuers with higher levels of debt. The more an issuer or sector borrows, the greater the tilt toward that issuer in the index. Leverage and creditworthiness are negatively correlated, so a value-weighted index will be more susceptible to credit quality deterioration than an equally weighted index will be.

Question 88

Liability-Driven Investing (LDI) and Asset-Driven Investing (ADL) are special cases of Asset-Liability Management (ALM). Explain the key differences. SS 10

Answer 88

The key difference is that with ADL, the assets are given and the liabilities are structured to manage interest rate risk; whereas with LDI, the liabilities are given and the assets are managed. All ALM strategies require the manager to incorporate the interest rate sensitivity of both the assets and the liabilities in the portfolio management process.

Question 89

What is the formula for convexity? SS 10

Answer 89

Convexity = (Macaulay Duration² + Macaulay Duration + Dispersion)/(1 + Cash Flow Yield)²

Question 90

What is the formula for Effective Duration? SS 10

Answer 90

Effective Duration = (PV_-) - (PV₊) / (2 x Curve x PV₀)

Question 91

How do you calculate the notional principal (NP) on an interest rate swap needed to close an asset-liability duration gap to zero

Answer 91

Asset BPV + (NP x (Swap BPV/100)) = Liability BPV Solve for NP

Question 92

Are investment grade bonds more or less sensitive to interest rate changes and credit migration than high yield bonds?

Answer 92

Investment-grade bonds have lower credit and default risks than high-yield bonds and are more sensitive to interest rate changes and credit migration, which cause credit spread volatility. The much higher credit loss rate experienced with high-yield bonds results in an emphasis on credit risk and the market value of the position to evaluate high-yield risk.