CFA 2018 level 3 gostudy CFA l3 equation guide for 2017

Behavioral Finance CAPM Model ?? = ?? + ??? − ?? Where: re = The required return on equity rf = Risk-free rate rm = The market return β = The stock market beta rm-rf = The Equity risk P

Guided Notes for CFA® Level 3 – 2017

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GoStudy’s CFA Level 3 – 2017 Exam Equation Sheet

Contents

Behavioral Finance 4

Private Wealth Management 4

Taxes & Private Wealth 5

Estate Planning 7

Institutional Investors 8

Capital Market Expectations 8

Capital Market Expectations – Financial Equilibrium Models 9

Equity Market Valuation 10

Relative Valuation Models 11

Asset Allocation 12

Fixed Income 13

Bond Portfolio Management 14

Interest Rate Swaps & Options 15

International Bond Returns 15

Equity Portfolio Management 16

Alternatives 17

Risk Management 18

Currency Risk Management 19

Risk Management with Futures & Forwards 20

Options 21

Swaps 22

Portfolio Execution 22

Monitoring & Rebalancing 23

Return Calculations 23

Global Investment Performance Standards 25

Behavioral Finance

CAPM Model

𝑟𝑒 = 𝑟𝑓 + 𝛽(𝑟𝑚 − 𝑟𝑓) Where:

re = The required return on equity

rf = Risk-free rate

rm = The market return

β = The stock market beta (rm-rf) = The Equity risk Premium (ERP)

Behavioral Asset

Pricing Model

(BAPM)

𝑟𝑒= 𝑟𝑓+ 𝛽(𝑟𝑚− 𝑟𝑓) + 𝑠𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 The more analysts disagree, the wider the sentiment premium Private Wealth Management

Solving for

Required

Return on IPS

question

 List the client objectives

 Quantify their current assets This is their PV

 Calculate the time horizon This is n

 Calculate what they will need on an annual basis This is their PMT This

is sometimes a predictable annual payment (like a mortgage) or the sum of their total living expenses (think time value) NET of their income (so total inflow or outflow)

Make sure you apply nominal/real and pre/post tax to these inputs as well

 Calculate their FV This is often equal

to the PV adjusted for inflation over the time horizon

 Calculate the % return needed This will be using your financial

calculator

 Are you solving for after tax

or before tax returns?

 If you are solving for nominal return (most likely) are you including expected inflation?

 Have you adjusted the PV (current investable assets)

to account for immediate cash inflow/outflow?

 Have you adjusted next year’s required cash flows (CF) for inflation if needed? Are you using the correct (+/-) signs when adjusting for cash in and out?

 Have you adjusted the PV to account for any immediate cash flows in or out?

Taxes & Private Wealth

Key Principles:

 The less you trade the more efficient your tax efficient your portfolio will be

 The longer you can defer paying taxes the more your overall portfolio will benefit (tax

alpha)

 Relative tax rates matter when comparing future/terminal values

Where FVIF = Future value interest factor

-The percentage of total taxes paid is

> than the stated tax rate (due to compounding)

-As you increase the investment time horizon (N), the tax drag increases

in both $ and % terms -As you increase the investment returns (R), the tax drag increases in both $ and % terms

-The loss to deferred taxes is always

a constant rate regardless of time or return

-Tax rate = tax drag % -Thus the value of deferring taxes increases as the time or return increase

Deferred Capital

Gains Tax (MV ≠

Cost Basis)

𝐹𝑉𝐼𝐹𝐶𝐺𝐵= [(1 + 𝑟)ⁿ(1 − 𝑡𝑐𝑔)] + 𝑡𝑐𝑔𝐵

B = Cost Basis/Market Value

-The lower the cost basis relative to current market value the more taxes you will pay

-As with accrual taxes the longer the time period the greater the tax drag

% -UNLIKE accrual taxes, the greater the returns the lower the tax drag %

Deferred capital gains Less tax drag (greater impact of deferring payment) Less tax drag (greater impact of deferring payment)

Blended Tax Impacts

PI = Proportion or weight of total return

Realized Tax

Rate realized tax rate = PITI+ PDTD + PCGTCG

PI = Proportion or weight of total return from each source (Interest, Dividends, Capital Gains) The Ts are the tax rates

-Adjusts the capital gains tax rate gain to reflect previously taxed dividends, income and realized capital gains so that they will not be double taxed

- Numerator is (1 – all individual proportions of returns) and the Denominator is (1 – realized tax rate)

or IRR, that connects PV and FV -Use your financial calculator to solve for I/Y by plugging in FV, PV, and N I/Y represents the geometric average return for the period in question

Estate Planning

Relative value of tax

free gift vs bequest

𝐹𝑉𝑇𝑎𝑥−𝑓𝑟𝑒𝑒 𝑔𝑖𝑓𝑡

[1 + 𝑟𝑔(1 − 𝑡𝑖𝑔)]ⁿ [1 + 𝑟𝑒(1 − 𝑡𝑖𝑒)]ⁿ(1 − 𝑇𝑒)

rg = Pre-tax return if asset is gifted and held by the recipient

tig = The recipient’s tax rate

re = Pre-tax return if asset is held by the testator/estate (r e is usually equal to rg)

tie = The giftor (testator)’s tax rate

Te = The estate tax rate

Calculating Core Capital Needs

Core capital is defined as the amount of assets needed to meet liabilities plus a reserve for

unexpected needs Excess capital is whatever is left over

Core capital needs are calculated as:

𝑃𝑉(𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑛𝑒𝑒𝑑) = ∑ 𝑝(𝑆𝑢𝑟𝑣𝑖𝑣𝑎𝑙𝑗) 𝑥 𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔𝑗

(1+𝑟)𝑗

𝑁 𝑗=1

Where

𝑝(𝑠𝑢𝑟𝑣𝑖𝑣𝑎𝑙) = 𝑝(𝐻𝑢𝑠𝑏𝑎𝑛𝑑 𝑠𝑢𝑟𝑣𝑖𝑣𝑒𝑠) + 𝑝(𝑊𝑖𝑓𝑒 𝑠𝑢𝑟𝑣𝑖𝑣𝑒𝑠)

− [𝑝(𝐻𝑢𝑠𝑏𝑎𝑛𝑑 𝑆𝑢𝑟𝑣𝑖𝑣𝑒𝑠) 𝑥 𝑝(𝑊𝑖𝑓𝑒 𝑠𝑢𝑟𝑣𝑖𝑣𝑒𝑠]

Institutional Investors

Spending Rules

Spending rules are used to determine how much money an endowment needs to spend in its next

year which means they can come up as part of a return calculation The less variable the spending

the more risk an endowment can take all else equal

For all of the equations listed below S=the specified spending rate, R = smoothing rate (given)

i=inflation, and MV = market value

Three Year Average

3

Geometric Spending Rule 𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔 = (𝑅)(𝑆𝑝𝑒𝑛𝑑𝑖𝑛𝑔𝑡−1)(1 + 𝑖𝑡−1) + (1 − 𝑅)(𝑆)(𝑀𝑉𝑡−1)

Capital Market Expectations

𝑃0 = this year’s share price

𝑔 = REAL earnings growth

Grinold & Kroner

(𝐷𝑖𝑣1

𝑃0 ) − ∆𝑆

𝑅 𝑖 = expected return 𝐷𝑖𝑣 1 = next year’s expected dividend

𝑃 0 = this year’s share price

𝑔 = REAL earnings growth

𝑖 = inflation

∆𝑆 = Percentage Change in outstanding shares, negative (-∆S) when there are share repurchases whereas ∆S is positive when number of shares outstanding increases

Capital Market Expectations – Financial Equilibrium Models

investable market (gim)

Solving for ERP in

ICAPM

𝐸𝑅𝑃𝑖 = 𝜌𝑖,𝑚𝜎𝑖 ∗ 𝐸𝑅𝑃𝐺𝐼𝑀

𝜎𝑚Note that 𝐸𝑅𝑃𝐺𝐼𝑀

2 Calculate the ERP of the market assuming it is fully segmented from the global portfolio (i.e

ignore the correlation with the global market)

𝐸𝑅𝑃𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑 = 𝜎𝑖∗𝐸𝑅𝑃𝐺𝐼𝑀

𝜎𝑚

3 Weight the results of Step 1 and Step 2 based on the actual level of market integration (which

will be given on the exam)

𝐸𝑅𝑃𝑃𝑎𝑟𝑡𝑖𝑎𝑙 𝑆𝑒𝑔𝑚𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛= 𝑤𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑𝐸𝑅𝑃𝑖𝑛𝑡+ (1 − 𝑤𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑)𝐸𝑅𝑃𝑠𝑒𝑔

4 Add any illiquidity premium to the weighted average from Step 3 This final number will be the

expected return for the market in question

Taylor Rule

𝑟𝑡𝑎𝑟𝑔𝑒𝑡 = 𝑟𝑛𝑒𝑢𝑡𝑟𝑎𝑙 + [0.5(𝐺𝐷𝑃𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑− 𝐺𝐷𝑃𝑡𝑟𝑒𝑛𝑑)

+ 0.5(𝑖𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑− 𝑖𝑡𝑎𝑟𝑔𝑒𝑡)]

Where:

𝑟𝑡𝑎𝑟𝑔𝑒𝑡 = the target short-term interest rate

𝑟𝑛𝑒𝑢𝑡𝑟𝑎𝑙 = the short-term rate that would be targeted if GDP was

on trend and inflation was on target 𝐺𝐷𝑃𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 = the forecasted GDP growth rate 𝐺𝐷𝑃𝑡𝑟𝑒𝑛𝑑 = the long term, observed GDP trend growth rate

𝑖𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 = the forecasted inflation rate

𝑖𝑡𝑎𝑟𝑔𝑒𝑡 = the target inflation rate

 If expected GDP < GDP trend then the central bank should cut rates to stimulate the economy

 If expected inflation > target inflation then the central bank would raise rates

to minimize inflation

Equity Market Valuation

Y is GDP

L is the quantity of labor

K is the quantity of capital

A is a positive constant representing technology/total factor productivity (Solow residual)

α is the output elasticity of capital and is a number between 0 and 1 and (1-α) is the output elasticity of Labor Sometimes it is also called β

The H Model

𝑉0 = 𝐷0

𝑟 − 𝑔𝐿[ (1 + 𝑔𝐿) + 𝑁

2 (𝑔𝑆 − 𝑔𝐿) ] Where N = # years, gL = long term growth rate, gS = short term growth rate

Relative Valuation Models

Fed Model

𝑆&𝑃 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑦𝑖𝑒𝑑 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑦𝑖𝑒𝑙𝑑

Ratio > 1, Equities undervalued; Ratio < 1, equities overvalued; if the ratio = 1 then equities are fairly valued DISADVANTAGES: Ignores equity risk premium, ignores earnings growth, compares a real variable to a nominal one

E 1 = Next period’s earnings

P 0 = This period’s price

Y b = Yield on A rated corporate bonds

d = a subjective weighting for importance of earnings growth LTEG = the 5 year growth forecast for earnings growth

10 Year average

P/E

𝑃0

10 𝑦𝑒𝑎𝑟 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑆&𝑃 𝑟𝑒𝑎𝑙 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑦𝑖𝑒𝑙𝑑Compare to avg, if ratio > avg, overvalued, should decrease

Tobins Q

𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 =

𝑀𝑉𝐷𝑒𝑏𝑡 + 𝑀𝑉𝐸𝑞𝑢𝑖𝑡𝑦𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡

If the ratio is greater than 1 than the assets are overvalued and vice versa

(Shortfall risk is risk of exceeding a maximum acceptable dollar loss)

Roys Safety First

Criteria

𝑅𝑆𝐹 = 𝑅𝑃 − 𝑀𝐴𝑅

𝜎𝑃The higher the ratio the better

1 Solve for required return for a portfolio

2 You will then have a table with a list of other portfolios on the efficient frontier You’ll need to determine which two portfolios bracket your portfolio based on expected return (i.e one will be higher and one will

be lower than your required return)

3 Then solve for the weighted average of each bracketed portfolio you will hold

4 Check that maximum acceptable standard deviation is not exceeded

5 From there you can use those two portfolio weights to solve for each individual asset class weight in your portfolio or to determine your standard deviation

Note: The Tangency portfolio is one with highest Sharpe ratio

Fixed Income

Effective Duration

𝐷𝑃= ∑ 𝑤𝑖𝐷𝑖𝑛

𝐷𝑃 = the effective duration of the portfolio

wi = the weight of bond i in the portfolio

𝐷 𝑖 = the effective duration of bond i

𝑀𝑉 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑑𝑒𝑥

2 Now that we have the weight of that period’s contribution to the portfolio’s value

we need to convert that to its duration contribution To get the duration contribution we simply multiply the duration of a given period by its weight

Duration Contribution = Duration ∗𝑃𝑉 𝑜𝑓 𝑃𝑒𝑟𝑖𝑜𝑑𝑠 𝐶𝐹

1 Calculate the new DD of the portfolio

2 Calculate the rebalancing ratio to determine the required percentage change (cash needed) to restore the value of the portfolio

3 If needed, multiply the % change needed (rebalancing ratio – 1) by the market value

of the portfolio to calculate the necessary increase/decrease in dollar value

Bond Portfolio Management

Rp = return on portfolio

Ri = return on invested assets

B = amount of leverage

E = amount of equity invested

C = cost of borrowed funds

Leverage &

Duration

𝐷𝑃 = 𝐷𝑖𝐼 − 𝐷𝐵𝐵

𝐸Where:

Dp = duration of portfolio

Di = duration of invested assets

DB = duration of borrowed assets

I = amount of invested funds B= amount of leverage

E = amount of equity invested

Repurchase

Agreement

𝐷𝑜𝑙𝑙𝑎𝑟 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 = 𝑎𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑 ∗ 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 (𝑇𝑖𝑚𝑒 360⁄ )

Know the factors influencing the repo rate (+/-)

Bond Futures &

Duration

# 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠 𝑡𝑜 𝑏𝑢𝑦 𝑜𝑟 𝑠𝑒𝑙𝑙 = (𝑦𝑖𝑒𝑙𝑑 𝑏𝑒𝑡𝑎)(𝑀𝐷𝑇− 𝑀𝐷𝑃

𝑉𝑃(𝑃𝑓∗ 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟))

MDt = target modified duration, MDp = Portfolio MD, MDF = futures MDf)

 If we want to increase DD we BUY FUTURES

 If we want to decrease DD we SELL FUTURES

Hedge Ratio

ℎ𝑒𝑑𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑜𝑓 𝑏𝑜𝑛𝑑 𝑡𝑜 𝑟𝑖𝑠𝑘 𝑓𝑎𝑐𝑡𝑜𝑟

𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑡𝑜 𝑟𝑖𝑠𝑘 𝑓𝑎𝑐𝑡𝑜𝑟

If the bond has greater risk exposure than the futures, you would need more futures

contracts to fully cover the risk

Yield Beta

𝑦𝑖𝑒𝑙𝑑 = 𝛼 + 𝛽(𝑦𝑖𝑒𝑙𝑑 𝑜𝑛 𝐶𝑇𝐷) + 𝜖 Yield Beta measures the sensitivity to interest rate changes of the CTD bond versus the original bond You’ll use the value when using futures to modify a portfolio’s duration

Interest Rate Swaps & Options

Forward 𝐹𝑉 = (𝑠𝑝𝑟𝑒𝑎𝑑 𝑎𝑡 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 − 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑠𝑝𝑟𝑒𝑎𝑑) ∗ 𝑛𝑜𝑡𝑖𝑜𝑛𝑎𝑙 ∗ 𝑟𝑖𝑠𝑘 𝑓𝑎𝑐𝑡𝑜𝑟 International Bond Returns

Equity Portfolio Management

Returns-based

Style Analysis

𝑅𝑃 = 𝑏0+ 𝑏1𝑆𝐶𝐺 + 𝑏2𝐿𝐶𝐺 + 𝑏3𝑆𝐶𝑉 + 𝑏4𝐿𝐶𝑉 Where:

Rp = returns on manager’s portfolio SCG = returns on a small-cap growth index LCG = returns on a large cap growth index SCV = returns on a small cap value index LCV = returns on a large cap value index The weight of each coefficient (beta) is non-negative and together they sum to

1 R2 is the coefficient of determination, and it shows the percentage of an investor’s returns explained by the style indices Here, 1-R2 is the amount of the returns unexplained by style In other words, 1-R2 shows us the percent of returns due to the manager’s ability to select securities

IR = the information ratio

IC = the information coefficient

𝑅𝑓 = Risk free rate

𝛿 = Lease rate Forward markets will be in contango if 𝛿1< 𝑅𝐹

T = Time Forward markets will be in backwardation if 𝛿 1 > 𝑅 𝐹

Commodity Futures

Price with Storage

Costs

𝐹0,𝑇 = 𝑆0𝑒(𝑅𝑓 +λ)𝑇 (continuous compounding) Where λ = storage cost

𝐹0,𝑇 = 𝑆0𝑒(𝑅𝑓 )𝑇+ λ0,𝑇 (discrete cost) where λ𝑜,𝑇 = FV storage costs

Commodity Futures

Price with

Convenience Yield

𝐹0,𝑇 = 𝑆0𝑒(𝑅𝑓 +λ−c)𝑇 where c = the convenience yield The lease rate is the convenience yield – storage costs: 𝛿 = 𝑐 − λ

Commodity Futures

Price Relationship

with Return factors

 𝑅𝑓↑; 𝐹𝑃 ↑ as financing costs are avoided

 λ ↑; FP ↑ as storage costs are avoided

 𝛿 ↑; 𝐹𝑃 ↓ as you lose the opportunity to earn the lease rate

 𝑐 ↑ 𝐹𝑃 ↓ as it impacts ability to engage in a reverse cash & carry strategy

Where FP = Futures Price and FDF = Future Discount Factors, which are equal to 1 ⁄(1 + 𝑟)𝑇