portfolio management and wealth planning formulas

7/29/2019 Portfolio Management and Wealth Planning Formulas

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Portfolio Management andWealth Planning

Book =1 Study Session = 3 & 4 Reading = 7

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Where:

P (AIB) = probability of event A occurring given that event B has occurred; Conditional

probability of event AP (BIA) = probability of event B occurring given that event A has occurred; conditional

probability of event BP (B) = unconditional probability of event B occurringP (A) = unconditional probability of event A occurring

Marginal Tax Rate = the individual's marginal tax rate is simply the highest tax rate

applied.

Average Tax Rate = Total Taxes Paid / Total Taxable Income

Investment income tax (accrual taxes):

T1 = Annual Tax rate on investment income

R = Before Tax investment return

N = Number of periods

Gain after Accrual Taxes = After Tax Future Value initial investment

Gain lost to Tax (Tax Drag) = Gain with no Tax Gain after accrual taxes

Tax Drag = (Gain after accrual taxes / Gain with no tax)

Deferred capital gains tax (MV = cost basis):

Tcg = Tax rate on capital gain

Deferred capital gains tax (MV # cost basis):

FVIFCGBT = [(1 + R)N(l - T CG)] + TcGB


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B = ratio of cost base with market value

Wealth-based tax: FVIFwT = [(1 + R) (l - TW)]N

Tw = wealth based tax

Tax drag is based on both principal and returns

Realized tax rate =

Effective capital gains tax rate:

Future value interest factor after all taxes:

Accrual Equivalent after Tax Return

Accrual Equivalent Tax Rate

Future value interest factor for a tax-deferred account (TDA):

R = before tax return on account

Tn = Tax rate in effect at the time of withdrawal


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Future value interest factor for a tax-exempt account:

Accrual Equivalent Tax Rate:

Objective function for allocation of risky assets:

Relative after-tax value:

= rg pre-tax return earned on an asset

= tig applicable income tax rate

= Te Estate Tax rate

= Tg Gift tax rate

When Tax paid by Donor then value of Gift will be:

Donor will pay the tax


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Generation skipping:

Double taxation: effective tax rates:

An individual living in a country that bases income tax on residency has total worldwide income

of1 ,500,000. 600,000 of that amount is generated in a source jurisdiction country. The

domestic country charges 40% income taxes on worldwide income and the source country

charges 35% taxes on income generated within its borders.


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Credit Method:

Tcredit =Max(Tresidence' Tsource) =Max(40%, 35%) =40%If you are asked for total taxes paid as well as the amounts receivedby each country on theforeign source income, don't forget the domestic income.This person will have to pay 900,000 x

0.40 = 360,000 on the domestic income inaddition to taxes paid on the foreign source income.

Note that she pays total taxes of1, 500,000 x 0.40 = 600,000: 360,000 + 30,000 = 390,000 to thedomestic countryand 2 1 0,000 to the foreign country.

Exemption Method:

Under the exemption method, income generated in a source country is totally exempt from

domestic taxation.

Domestic taxes on the foreign income = 0

Domestic taxes on the domestic income = 900,000 x 0.40 = 360,000

Foreign taxes on foreign-generated income = 600,000 x 0.35 = 21 0,000

The individual's total taxes are 360,000 + 21 0,000 = 570,000 rather than 600,000 as under the

credit method.

Deduction Method:Under the deduction method, the individual is allowed to deduct the taxes paid to the foreign

source country from taxable income.T deduction = Tresidence + Tsource (l - Tresidence) = 0.40 + 0.35(1 - 0.40) = 0.61 =61 o/o

Total foreign source income = 600,000.

Taxes paid to the source country = 600,000 x 0.35 = 21 0,000.

Foreign source income taxed by domestic country = 600,000 - 21 0,000 = 390,000.

Domestic taxes on foreign source income = 390,000 x 0.40 = 156,000.

Tax rate on foreign income = (21 0,000 + 156,000) I 600,000 = 61 o/o.

The individual pays taxes on the domestic income of 900,000 x 0.40 = 360,000 for total world-

wide taxes of 360,000 + 21 0,000 + 1 56,000 = 726,000.


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Book =2 Study Session = 5, 6, 7 & 8 Reading

= 15 22

ENDOWMENTS AND SPENDING RULES:

S = the specified spending rate

Rolling 3-year average spending rule

Geometric spending rule:

Where:

R = smoothing rateI = rate of inflationS = spending rate

Bank Risk Measures:

Where:LADG = leverage adjusted duration gapDassets = duration of the bank's assetsDliabilities = duration of the bank's liabilitiesL / A= leverage measure (market value of liabilities over market value of assets)

Zero, equity should be unaffected by interest rate changes. Positive, equity change is inverse to rates (e.g., rates up equity down). Negative, equity value moves in the same direction as rates.

Ba = Firms operating asset beta

WACC = RF + Ba(MRP)The firm's total asset beta is equal to the weight of owners' equity in the balancesheet multiplied by the firm's equity beta

The Firm's Operating Beta and WACC


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Operating Asset Beta

[Total Asset Beta (Pension Asset weight ) * (Pension Beta)] / Operating Asset Weight

Weight of debt = 1 - weight of owners' equity

D/ E = weight of debt / weight of owners' equityWeight of Equity = Beta of Total Assets / Beta of Equity

A model developed by JP Morgan states that volatility in the current period t, is a weighted

average of the previous periodvolatility t-1, and a random error is last.

The term 0 measures the relationship, or rate of decay, between volatility in one period to the

next.

Covariance of two markets:

Ri = expected return on stock iDiv1 = dividend next periodPo = current stock priceg = growth rate in dividends and long-term earnings

R1 = expected return on stock i; referred to as compound annual growthrate on a Level III exam

= expected dividend yieldI = Expected Inflation

G = growth rate

= Percentage change in shares outstanding (positive or negative)

= percentage change in the PIE ratio (re pricing term)

Expected Income Return:

= Expected dividend yield percentage change in shares outstanding (positive or negative)

Expected nominal earnings growth = ( i + g)


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Expected Repricing Return =Ri = exp (income return)+ exp (nominal earnings growth)+ exp (repricing return)

Expected current yield (income return) = dividend yield + repurchaseyield

Expected capital gains yield = real growth + inflation + re-pricing

Where:

Ri = expected return on asset i

Rp = risk-free rate of returnBeta = sensitivity (systematic risk) of asset i returns to the global investable market

R M = expected return on the global investable market

Ri -Rf = ,Bi (Rm - Rf)Denoting R i - R F as RPi

So replace beta with this given information

Taylor Rule; Target interest rate to achieve neutral rate:


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Cobb Douglas Production Function (CD):


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If the S&P 500 earngins yield is higher than the Treasury yield, index vlaue is too low

relative to earnings so equiteis are undervalued should increase in value.

Internsic Value


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Utility-adjusted Return:

Roys Safety-First Measure

Determining Whether to Add an Investment to the Portfolio:


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Variance of the returns on the foreign asset in U.S. dollar terms;


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Book =5 Study Session = 16, 17 & 18

Reading =39 43

Effective spread for a buy order = 2 x (execution price mid quote)Effective spread for a sell order = 2 x (mid quote - execution price)

Total Implementation Shortfall:

Explicit Costs:

Missed Trade Opportunity Cost (MTOC):

T = Target Allocation

P = Percentage change in that allocation

M = M is the constant proportion of the cushion invested in equities

Cash Flow at the Beginning of the Evaluation Period:

Cash Flow at the End of the Evaluation Period:


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Time-Weighted Rate of Return:

The Rooney account was $2,500,000 at the start of the month and$2,700,000 at the end. During the month, there was a cash inflow of$45,000 on day 7 and $25,000 on day 1 9 . The values of the Rooneyaccount are

$2,555,000and

$2,575,000(inclusive of the cash flows for the

day) on day 7 and day 19, respectively. Calculate the time weighted rate of return(assuming 30 days in the month).Sub period 1 (days 1-7)

Sub period 2 (days 8-19)

Sub period 3 (days 20-30)

TWRR = (1 +0.004) (1 - 0.002) (1 +0.049) - 1 = 0.05 1 =5. 1 o/o

Money-Weighted Rate of Return:


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Factor Model Based:

A = P B

S = B M

A = excess retrun attributable to the managements active management decsions

P = Investment managers portfolio returnB = benchmark retrun

S = excess retrun attributable to the managers investment style

M = retrun on market

Incremental return to the asset category level:


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Incremental return at the benchmark level:

Return to the investment managers level:

Micro performance attribution:


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and

The Treynor Measures:

The Sharpe Ratio:


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Information Ratio (IR):


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Security Selection Effects:

Global Return Decomposition:

Now broken down the capital gains component of the portfolio into market return and

security selection,


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Benchmark Domestic Return:


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2-period return to active management

Security Selection Effect:

Market Allocation Effect:

The Correct Method:


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Standard Deviation or Total or Absolute Risk:

Tracking Error or Relative Risk:

Original Dietz Method:

Modified Dietz Method:


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portfolio management and wealth planning formulas

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