CFA Glossary

The Financial Journal

2015-10-31T08:29:00.000+09:00

To all readers of this blog,

Thank you very much for visiting and reading this blog. That would be great if you could also come visit this blog. I'm going to publish articles for investment management professionals and about what I'm interested in.

"The Financial Journal"
http://thefjg.blogspot.com

Portfolio Management with the R Programming Language

2015-06-17T16:12:00.002+09:00

Portfolio Management with the R Programming Language

http://pmwr.blogspot.com

VWAP and Implementation Shortfall (IS)

2015-05-19T14:46:00.000+09:00

**VWAP and Implementation Shortfall Algorithm (IS): preferable condtions**
	VWAP	IS
Participation rate (*1)	Low	Low
Bid-Ask Spread	Narrow	Narrow
Urgency to complete trade	Low	High

(*1) (One's order volume) / (Average daily volume traded)

Duration of Interest Rate Swap

2015-05-19T09:45:00.001+09:00

Approximation (at the beginning of the contract or right after the interim interest rate payment):

D_{Receive-Fixed, Pay-Float} = +(75%)(T) -(50%)(T_Float)

D_{Receive-Float, Pay-Fixed} = +(50%)(T_Float) -(75%)(T)

T: maturity of the interest rate swap
T_Float: payment frequency period of the floating leg (e.g., 0.50 year for semi-annual payment frequency)

Financial Risk and Non-financial Risk

2015-04-28T08:28:00.000+09:00

Financial Risk (*1)

market risk (*3)
credit risk
liquidity risk

Non-financial Risk (*2)

operational risk
model risk
settlement risk
regulatory risk
legal risk
tax risk
accounting risk

(*1) all risks derived from events in the external financial markets
(*2) all other forms of risk
(*3) risk related to interest rates, exchange rates, stock prices, and commodity prices

Futures: Total Return

2015-04-26T20:09:00.001+09:00

Futures

(Total Return)

= (Roll Return) + (Spot Return) + (Collateral Return)

= (Changes in futures price) - (Changes in spot price) + (Changes in spot price) + (Collateral Return)

= (Changes in futures price) + (Collateral Return)

Contingent Immunization

2015-04-19T11:11:00.001+09:00

You can use the entire fixed-income portfolio for active management until the portfolio drops below the safety net level or the terminal value.

Repo Rate

2015-04-19T10:00:00.001+09:00

Factors that affect repo rates:

Quality of collateral
- Illiquid: higher borrowing costs
- Special collateral: lower borrowing costs (thanks to high demand for the special collateral)
Short sellers' positions
- Demand / availability of the collateral: short sellers' needs can affect the demand / availability of the collateral, and hence the repo rate, when the lender of the funds needs the collateral for a short sale.

Horizon matching

2015-04-14T21:29:00.001+09:00

Horizon matching:

(1) duration-matched

(2) cash flow-matched in the first few years (*)

(*) reduces the risk associated w/ non-parallel shifts of the yield curve

Immunization

2015-04-14T21:26:00.001+09:00

PV (Assets) = PV (Liabilities)

D (Assets) = D (Liabilities)

Ddist (Assets) > Ddist (Liabilities) (*)

PV: present value

D: duration

Ddist: distribution of duration

(*) If the distribution of the duration of the assets is wider than that of the liabiltiries, the duration of the assets after a parallel yield curve shift (whether up or down) will envelope the durations of the liabilities after the shift. The immunization can be maintained, although rebalancing may be necessary.

Also, credit risk destroys the immunization match.

Most importantly, the risk to immunization comes from non-parallel shift in the yield curve.

Active currency management

2015-04-14T08:52:00.001+09:00

Active currency management, rather than a hedging ratio closer to 100% or a narrow discretionary band for currency exposures, is appropriate if:

Time horizon: long
Liquidity: no or few immediate needs
Assets: more equities, less fixed income (Bond portfolios are typically associated with hedge ratios closer to 100% than equity portfolios cuz bond investment is investing its denominated currency.)
Emerging market exposures: Yes, given these country's typically higher yields (carry trade) and often volatile exchange rates
Characteristics of the fund and the beneficial investor: do not argue for a conservative currency strategy

Asset Class: adding a new asset class to an existing portfolio

2015-04-09T08:39:00.002+09:00

(SR)_i >(ρ)_i,P* (SR)_P
_{i: new asset class to be added to an existing portfolio}
_{P: existing portfolio}
(SR)_i: Sharpe Ratio of the new asset class
(SR)_P: Sharpe Ratio of the existing portfolio
(ρ)_i,P: correlation of returns of i and P

Asset Classes

2015-04-09T06:09:00.001+09:00

Asset classes should be:

Homogeneous
Mutually exclusive
Diversifying
Preponderance of world investable wealth
Sufficient from Capacity perspective

Roy's Safety First Ratio (Criterion)

2015-04-08T09:25:00.002+09:00

(Roy's Safety First Ratio)_i = (R_i - R_Threshold)/σ_i

R_i= (expected) return of a portfolio i
R_Threshold= threshold return (e.g., minimum acceptable return)
σ_i = standard deviation of return of a portfolio i

Utility Function

2015-04-08T09:22:00.001+09:00

U_i = r_i - (0.005) * (R_A) * (σ_i)²

U_i : utility (%) -- For instance, expected return = 5.5% should be treated as "5.5," rather than 0.055.
r_i : expected return (%)
R_A : risk-aversion (from 1 to 8, where 8 represents the highest degree of risk aversion )
σ_i : standard deviation (volatility of the expected return) (%)

Goat-based planning

2015-03-21T11:06:00.000+09:00

**Goal-based planning**
Risk Bucket	Personal	Market	Aspirational
investment instruments	personal residence cash equivalents treasury securities other safe investments	stocks bonds	privately owned business commercial and investment real estate concentrated stock positions (*)
goal	Protection from poverty or a decrease in lifestyle	Maintain the current standard of living	The opportunity to increase wealth substantially.

Goal-based planning allows an adviser to incorporate psychological considerations into the asset allocation and portfolio construction process.
Primary capital = Personal + Market

**(*) tools for addressing a concentrated positin**
#			example
1	outright sale	sell the concentrated position typically results in significant tax liabilities
2	monetization	provides the owners w/ funds to spend or reinvest w/out trigerring a taxable event	a loan against the value of a concentrate position
3	hedging	hedge w/ derivatives	a long put position

IPS (Investment Policy Statement)

2015-03-14T09:34:00.000+09:00

IPS

Objective

Return

assets

cash
residence
financial assets like stock (options)
insurance

liabilities

debts
retirement / educational needs

equity

IS (including inflation)

income

salary & bonuses, other compensations
pension and other benefits

ongoing expenses

living expenses
medical expenses
educational expense

Risk

willingness

psychological tolerance level, personality (e.g., aversion to loss, conservative investments)
experiences (e.g., adverse experience w/ creditors)
whether or not work to have continued compensations

ability

life cycle
fiscal tolerance level
concentrated holdings?
future assets like inheritance / trust?
any expenses for families? (e.g., medical expenses)

overall

willingness + ability

Constraints

Liquidity

ongoing expenses
cash reserve (w/ size, purpose)

Legal & Regulatory
Time Horizon

# of stage
duration of each stage

Taxes

income taxes, capital gain taxes
low-basis (book value) holding w/ possible future capital gain taxation
accumulated losses to offset taxes on future realized gains

Unique Circumstances

health condition (of family members)
any education costs? (for children)
any investment needs? (e.g., investments for children's business, setting up a charitable foundation)
concentrated positions?

When selecting a portfolio, choose one with:

Expected return above minimum required return (including inflation)
Highest return / risk efficiency (e.g., Sharpe Ratio = ((Expected return) - (Risk-free rate))/(SD of return))
Balanced income (stability) and gain (growth prospects). (Most) broadly diversified.
A total return approach that combines capital appreciation and capital preservation

Behavioral Biases

2015-03-08T16:21:00.003+09:00

Behavioral Biases

Behavioral biases

Cognitive errors (faulty reasoning, statistical / info-processing / memory errors) (*1)

Belief perseverance (maintain beliefs)

Conservatism
Confirmation
Representativeness
Illusion of control (*4)
Hindsight

Info-processing

Anchoring and adjustment
Mental accounting
Framing
Availability

Emotional biases (reasoning influenced by feelings) (*2)

Loss aversion

Disposition effect (*3)

Overconfidence (*5)

Self-attribution
Illusion of knowledge

Self-control
Status quo (*6)
Endowment
Regret aversion

(*1) more easily corrected; to be reduced or eliminated
(*2) heard to correct; to be adaptedadjusted

(*3) holding on to losers

(*4) The more info/data, the more thorough.

(*5) possibly due to familiarity

(*6) possibly due to naive extrapolation of past returns

-----

Unclassified

Social proof: A belief in which individuals are biased to follow the beliefs of a group.

Herding: ditto

Halo effect: An impression created in one area influceses an opinion in another area.

Naive diversification: have a equal-weighted portfolio w/out rationality

Momentum: Partly explained by short-term under-reaction and long-term over-reaction. "Technical analysis has the potential to uncover opportunities where there are over- and under-reactions to relevant info."

Loyalty effects: e.g., a stock of a past employer

Cognitive errors

Gambler's fallacy: A faulty understanding about the behavior of random events. (e.g., "We lost in five consecutive days. It's rare considering its probabilities. So we should be able to win next time.")

Emotional biases

Home bias: It occurs when investors exhibit a strong bias in favor of domestic securities in the context of global portfolios.

Residence-Source Tax Conflict

2014-12-18T19:14:00.001+09:00

**Residence-Source Tax Conflict**
method	Source Tax Rate	Residence Tax Rate	Total Tax Rate
credit	T_Source	0	T_Source (*)	If T_Source > T_Residence
credit	T_Source	(T_Residence - T_Source)	T_Residence (*)	If T_Source < T_Residence
exemption	T_Source	0	T_Source
deduction	T_Source	(1 - T_Source)* T_Residence	T_Source + (1 - T_Source)* T_Residence

(*) TCredit = Max (T_Source, T_Residence)

In each case, the source country receives full taxes on income generated within its borders. Differences in domestic country (=residence) taxes arise from different handling of foreign (=source) taxes.

Relative After-Tax Values of Gifts

2014-12-17T18:16:00.000+09:00

**Relative After-Tax Values of Gifts**
gift	pre-tax	applicable tax rate
receiver	r_r	t_ir
donor	r_d	t_id

T_E = estate tax rate (and would be paid by the grantor from the estate when bequests); if paid by the recipient, then it's called the inheritance tax
T_G = gift tax rate (paid by the giver or the donor)
n = time horizon

**Relative After-Tax Values of Gifts**
	Relative After-Tax Values of Gifts	description
definition	(FV_{taxable gift})/(FV_bequest)
tax-free gift	[1+r_r(1-t_ir)]ⁿ -------------------------------------------- [1+r_d(1-t_id)]ⁿ* (1-T_E)	T_G=0
taxable gift, T_Gpaid by the receiver	[1+r_r(1-t_ir)]ⁿ* (1-T_G) -------------------------------------------- [1+r_d(1-t_id)]ⁿ* (1-T_E)
taxable gift, T_Gpaid by the donor	[1+r_r(1-t_ir)]ⁿ* (1-T_G+T_GT_E) -------------------------------------------- [1+r_d(1-t_id)]ⁿ* (1-T_E)	(*)
charitable gift	[1+r_r]ⁿ+ (T_oi) * [1+r_d(1-t_id)]ⁿ* (1-T_E) -------------------------------------------------------- [1+r_d(1-t_id)]ⁿ* (1-T_E)	(**)

(*) A taxable gift grows from 1 to [1+r_r(1-t_ir)]ⁿ, on a pre-tax basis in n years.
Considering the gift tax, paid by the donor, the taxable gift grows from (1-T_G) to [1+r_r(1-t_ir)]ⁿ* (1-T_G), under the receiver's management.
In this case, let's think about the situation that the donor has the gift and the estate. The donor gives the gift to the receiver and pays the gift tax by him/herself from the estate. The amount of the gift tax is subtracted from the estate. The reduction of the estate will cause the tax benefit; when the estate will be given to the receiver of the gift eventually, the less estate, the less estate tax burden. The amount of the tax reduction, which is a part of the estate, will also grow in n years. So there should be the second term which means this tax-benefit:
(1-T_G)* [1+r_r(1-t_ir)]ⁿ + (T_G)* [1+r_r(1-t_ir)]ⁿ* (T_E)

(**) The receiver is a tax-exempt charity.

T_oi = tax rate on ordinary income of the donor who is taxable.

Taxes and Investment Risk

2014-12-07T11:24:00.001+09:00

**Taxes and Investment Risk**
	Return	Risk(*)
Before-Tax	R_BT	σ_BT
After-Tax	R_AT = R_BT(1-T_n)	σ_BT(1-T_n)

(*) standard deviation of returns
T_n: the tax rate on investment income, at the year of n

If returns are high, the government receives more in taxes than when returns are low. In other words, part of the total variability of the investment is absorbed by the government.

If the investment is held in a tax-exempt account (TEA), such that the government has no stake in the investment, the investor bears all the investment risk.
This is also true for TDAs prior to withdrawals because annual returns are not subject to taxes.

Tax Profiles of Accounts

2014-12-06T16:19:00.001+09:00

**Tax Profiles of Accounts**
	Tax	Contribution	Return	Withdrawal	Withdrawal
AT	Accrual Tax (Account)	before-tax funds	taxed	taxed	FVIF_AT = [1+R_BT(1-T_n)]^N
CGBT	Deferred Capital Gains Tax (Account)	before-tax funds	unrealized capital gains: tax-free	taxed	FVIF_CGBT = (1+R_BT)^N-[(1+R_BT)^N-1](T_CG) - (1-B)(T_CG) = (1+R_BT)^N(1-T_CG) + (B)(T_CG)
TDA	Tax-Deferred Account (front-end loaded tax benefits)	before-tax funds	tax-free	taxed	FVIF_TDA = (1+R_BT)^N(1-T_N)
TEA	Tax-Exempt Account (back-end loaded tax benefits)	after-tax funds	tax-free	tax-free	FVIF_TEA = (1-T₀)(1+R_BT)^N (*)
WT	Wealth-Based Tax Account	before-tax funds	(both principal and return are) taxed	taxed	FVIF_WT = [(1+R_BT)(1-T_WT)]^N

(*) Assuming equivalent (1) contributions (after-tax for TEA), (2) returns, and (3) holding periods, the only difference in future values is that the government has a future tax claim on the TDA.

R_BT: before-tax return on the account
T_N: tax rate in effect at the time of withdrawal

T₀: current income tax rate

For TDA and TEA, a different result can arise if regulations limit the amount of deposit and the limit is the same for both TDA and TEA accounts. Even if the current and future tax rates are equal, the TEA can be superior.

Accrual Equivalent After-Tax Return, Tax Drag, and Accrual Equivalent Tax Rate

2014-12-06T09:15:00.003+09:00

An accrual equivalent after-tax return is the annual return that produces the terminal value as the taxable portfolio. (i.e., effective annual return) Accrual equivalent after-tax returns incorporate the effect of realised annual taxes as well as the deferred taxes that were paid at the end of the holding period.

FV_T = PV(1+R_AE)^N
FV_T : future value
PV : present value
R_AE : accrual equivalent after-tax return
N: time horizon (N periods)

(1+R_AE)^N = (FV_T / PV)
(1+R_AE) = (FV_T / PV)^(1/N)
R_AE = (FV_T / PV)^(1/N)- 1 (R_ART = return after realized taxes)

(Pre-tax Return) - (Accrual Equivalent After-Tax Return) = R - R_AE = (Tax Drag on the portfolio)

R ← R_AE (R_AE gets closer to the pre-tax return) when:

(Time horizon)↑ : Value of tax deferral increases with time.
(Deferred portfolio return)↑: Deferred realized return. The portfolio earns compound interest tax-free.

Accrual Equivalent Tax Rate

(R_AE)= R(1 - T_AE)
(T_AE) = 1 - (R_AE / R)

R_AE : accrual equivalent after-tax return

R: pre-tax return

T_AE : accrual equivalent tax rate

Think of it as the overall effective tax rates on the account, considering both accrual and deferred taxes.

The lower the T_AE, the more tax efficient the investment. Allocating more of your account to tax-efficient assets (e.g., growth assets with unrealized capital gains) pushes a greater percentage of your total return further out into the future, making the account more tax-efficient and producing a lower accrual equivalent tax rate.

Likewise, allocating heavily to tax-inefficient assets speeds up tax payments and increases the accrual equivalent tax rate.

Realized Tax Rate and Return After Realized Taxes

2014-12-01T10:19:00.001+09:00

V₀ = $100,000
V₁ = $110,000 (no additional contributions or withdrawals)
R = $110,000/$100,000 - 1 = 0.10 = nominal before-tax return

I = $300 = interest income received and reinvested into the portfolio
D = $4,000 = divided income received and reinvested into the portfolio
CG = $2,200 = realized capital gain; the proceeds from which were reinvested into the portfolio

**Realized Tax Rate and Return After Realized Taxes**
	(Un)realized gain $	Tax Rate	Tax $	Proportion of the total gain
I: Interest income	300	30%	90	300/10,000 = 0.03
D: Dividends	4,000	20%	800	4,000/10,000 = 0.40
CG: Realized capital gains	2,200	20%	440	2,200/10,000 = 0.22
Unrealized capital gains	3,500	20%		3,500/10,000 = 0.35
Total	10,000		1,330

Realized tax rate = T_Realized = (P_IT_I + P_DT_D + P_CGT_CG)
= (0.03*0.30 + 0.40*0.20 + 0.22*0.20)
= 1,330/10,000
= 0.1330 = 13.30%

Return after realized tax = R_ART = R * (1 - T_Realized)
= 0.10*(1 - 0.1330) = 0.0867 = 8.67%
= (($110,000 - $100,000) - $1,330)/$100,000
= ((110000 - 100000) - 1330)/100000
= 8670/100000 = 0.0867 = 8.67%

100000 * (1+ 8.67%) = $108,670

FVIF: Future Value Interest Factor

2014-11-30T15:20:00.004+09:00

R: pre-tax annual return
N: investment horizon in years

[1] Accrual Income Tax

FVIF_AT = [1 + R(1 - T_AT)]^N
[2] Deferred Capital Gains Tax

FVIF_{CG, MV≠Cost Basis} = (1 + R)^N- [(1 + R)^{N _}B](T_CG) = (1 + R)^N(1 - T_CG) + (B)(T_CG)
B: The ratio of cost basis to the current market value.

When MV = Cost Basis, then B = 1
FVIF_CG = (1 + R)^N- [(1 + R)^{N _}1](T_CG) = (1 + R)^N(1 - T_CG) + T_CG

[3] Wealth-Based Tax

FVIF_W = [(1 + R)(1 - T_W)]^N

[4] Effective Capital Gains Tax Rate

As we will see, deferred taxes will be greater (less) as less (more) accrual tax is paid annually.

T_ECG : Effective Capital Gains Tax Rate that adjusts for the annual taxes already paid.
T_ECG [1 - (P_I T_I + P_D T_D + P_CG T_CG)] = T_CG[1 - (P_I + P_D + P_CG)]

(P_I T_I + P_D T_D + P_CG T_CG) < (P_I + P_D + P_CG)
[1 - (P_I T_I + P_D T_D + P_CG T_CG)] > [1 - (P_I + P_D + P_CG)]
T_ECG < T_CG

In this example, we assume all dividends, interests, and realized capital gains were taxed and reinvested, and not subject to future taxations.

T_CG[1 - (P_I + P_D + P_CG)] = T_CG[P_{CG, unrealized}]
= T_ECG [1 - (P_I T_I + P_D T_D + P_CG T_CG)]

R_ART : Net Return After All Realized Taxes
R_BT : Before-Tax Return
R_ART = R_BT [1 - (P_I T_I + P_D T_D + P_CG T_CG)]

FVIF_ECG
= (1 + R_ART)^N- [(1 + R_ART)^N- 1](T_ECG) - (1 - B)(T_CG)
= [(1 + R_ART)^N(1- T_ECG)+ (T_ECG) - (1 - B)(T_CG)]

Future Value: FV_i = (V₀)(FVIF_i)
V₀: Initial Investment