CFA Level 3 Essentials

Private Wealth Management
need for cash reserve is liquidity requirement
if you are drawing from salary for expenses, there is no liquidity requirement. If you have a shortfall between salary and expenses, the difference will be made up by your return. That is a liquidity requirement.

In required return calculation, retirement income (pension income) taxed as ordinary income required return = cash needed / total investable assets
**Cash reserve is not part of cash needed

When answers reasons on IPS risk tolerance, look at the time horizon

Life insurance needs:
- high human capital - higher life insurance need
- less financial capital - higher life insurance need (financial wealth can be viewed as a substitute for life insurance)
- wage correlated to risky assets, the human capital value down -> less need for insurance

Payout of annuity
- payouts (income yields) higher when expected remaining longevity is shorter
- same age male and female, female have smaller payout bcoz of longer life expectancy than male
- 10 year period certain will reduce the payout
- 10 year period certain, small impact for 60 year old, big impact for 90 year old
- insurance company invest in bonds, when current yield on bonds are low, payout rates will be low.

variable annuity has less certainly about CFs bcoz they are linked to the performance of the underlying investment.

return objective is a sentence, eg: Return objective is to earn a rate of return enough to maintain the real value of assets and to support 25% of annual univ operating expenses
required return is calculation, eg: 5% + 4% + 0.55% = 9,55%

bounded rationality (satisficing) - meet the criteria specified but not necessarily optimal
prospect theory- loss averse
expected utility theory- risk averse

Friedman Savage utility function (risk evaluation is reference dependent)

- depending on wealth level and circumstances of decision maker

four axioms of utility theory: completeness, transitivity, independence, continuity

behavioral portfolio theory
investors construct portfolio in layers, portfolio may not be mean variance efficient.

goal based planning in concentrated position
personal risk bucket - protect from poverty
market risk bucket - maintain current standard of living
aspirational risk bucket - increase wealth substantial
* this goal three buckets do not take into account correlation among investments

personal risk bucket + market risk bucket = primary capital
aspirational risk bucket = surplus capital

mental accounting bias: ppl treat one sum of money differently from another sum, depends on which mental account money is assigned to
- cause placement of investment in different "buckets" w/o regard of correlation among the assets

Emotional Bias:
- Loss aversion bias: people tend to avoid losses, rather than achieving gains, risk seeking in losses, risk averse in gains
- overconfidence: people overestimate their knowledge and abilities
- self control bias: people fail to pursue long term goals because of lack of self discipline
- endowment bias: people value an asset more when they hold rights to it
- regret aversion bias: people tend to avoid making decisions, out of fear decision turn out poorly
- status quo bias: do nothing instead of doing something

Fixed Income
classic crossover trade where highest speculative grade bond (Ba1/BB+) are likely to benefit from an upgrade as economy strengthen

for an upward sloping yield curve, the immunization rate of return < ytm because of lower reinvestment return
1 yr spot rate 3%           
2 yr spot rate 5%           
50*1.03 + 50 = 101.50
(1101.50/1000)^(1/2) -1 = 4.9524%

Bonds:
Pure Indexing: full replication
enhanced indexing: match primary risk factors, match duration
enhanced indexing: minor risk factor mismatches, match duration
active management: larger risk factor mismatches, adjust duration slightly away from index's duration
full blown active management: mismatch on duration , and sector weight

primary risk factors: changes in interest rate, twist in yield curve, changes in spread

typical bond index is quite illiquid, pure bond indexing is much less common than pure equity indexing

The PV of the liability varies with interest rates, but the value when it is due, is fixed

The portfolio duration is weighted average of the duration of the bonds in the portfolio.

                                      Asset only       Liability relative
liability exposure           none                 term structure, inflation, growth
risk free investment       cash                 liability mimicking asset
low risk investment     low correlation    high correlation
                                      with assets       with liability

Investing in liability mimicking assets portfolio would not provide expected return greater than liability needs.
The challenge is to find most efficient way to allocate more to higher return assets while minimise risk versus liability
- hedge the liability using derivatives to mimic the market exposures of liability, use derivatives to hedge require less capital than cash investment. It frees up capital for higher return assets
- use the remaining capital for high return investment, using asset only approach

Immunization is a strategy used to minimise interest rate risk
classical immunization: process of structuring a bond portfolio that balances any change in value of portfolio with the return from reinvestment of coupon and principal through the investment period
1. bond portfolio duration = liability duration
2. PV of bond portfolio = PV of liability
Assumption: changes in yield curve are parallel, no default risk bcoz only investing in investment graded bonds

for multiple liability immunization
besides 1 and 2, add 3
3. distribution of durations of portfolio assets must have wider range than distribution of liabilities

In immunization plan, liabilities should be discounted using IRR of immunized portfolio.

Corp bond will not have lower cost of immunization bcoz corp bonds have default risk while immunization assumes no default risk. Use corp bond, raise the cost of immunization.

Also, corp bond is less liquid than T-bond, increase the cost of immunization .

cash flow matching require conservative rate of return assumption for ST cash, cash balance may be substantial. Funds from ash flow matching portfolio must be available when and before each liability is due, bcoz of difficulty in matching.

any portfolio consists of zero coupon bonds that mature at investment horizon has zero immunization risk
if CFs are concentrated aroidn horizon, reinvesmtnet risk and immunization risk are lower
if CFs are dispersed aroidn horizon, reinvesmtnet risk and immunization risk are higher

contingent immunization
- safety net value, cushion spread:  PV(assets) - PV(liabilities) is positive, can do contingent immunization with entire portfolio
- initial safety margin: PV(assets) - PV(liabilities) discounted on immunization rate

putable bonds offer a lower coupon than option free bonds given that  they provide a long option to bondholders. So they are not as sensitive to interest rates and when interest rate ↓, they offer less price appreciation. So putables do poorly when yields drop.

spread duration : % change in bond price for 1% change in its spread over treasure of same maturity,  for risky bonds, measure price changes when nominal spread changes

key rate duration: % change in bond price for 1% change in its ytm over treasure of given maturity, measure price changes when given par rate changes (and all other par rate remain unchanged)

Capital Market Expectation

High frequency data , suffers from asynchronism , or lack of sync –> lower correlation. For example, daily stock movement will have lower correlation than monthly stock movement.

Regime change results from monetary policy changes ot fiscal policy changes. Time period bias is the data is chosen to reflect a specific time. time period may not reflect the regime change.

low correlation reduce overall risk of the portfolio , but will not produce higher expected returns

Monte Carlo Simulation

advantage:

provide a distribution of probability of outcomes, than a point estimate

capture multi point effect of tax changes

disadvantage:

relies on historical data

does not incorporate changes of future financial environment

Fed model: 

Set LT treasure yield = S&P forward earnings yield

If LT treasure yield < S&P forward earnings yield  -> US stocks are undervalued

It ignores inflation and earnings growth

it can be applied to non-US equity market

it compare real earnings to nominal T-bond yield

It assume ROE =  treasure bond yield

Yardeni Model:

Set justified forward earnings yield = S&P forward earnings yield

(justified forward earnings yield)  E1/P0 = Yb - d*LTEG

it use corp bond yield, capture default risk premium, not the equity risk premium

CAPE:

use 10 year moving average P/E, uses 10 year moving average to control business cycle effects on earnings

CAPE = S&P index / real earnings

currency risk:

unhedged return = foreign bond return in local currency + currency return

hedged return = foreign bond return in local currency + f

                       forward discount/premium: f = (F - S) / S = id - if

hedged return = id + (rl - if)

ex-post risk is a biased measure of ex-ante performance

ex-post: use historical returns to predict the future risk

ex-ante: measurement before risk has occurred

(if historical prices reflected risk premium for event that did not occur, may overestimate ex-ante return)

resampled efficient frontier

- generate more stable portfolio

- generate more diversified portfolio

Black Litterman approach

- incorporate investor's views on the asset weights

- generate more diversified portfolio

PPP : exchange rate and inflation
current FX rate : THB/GBP = 51.482   annual inflation for next 5 year:Thailand 3.4% UK 1.9%

[1 +  ((1.034)^5-1) - ((1.019)^5 -1)] * 51.482 =

** need to be compounded by 5 years

It covers long term cuurency forecast.

IRP : exchnage rate and intrest rate

 (1 + id) = (S / F) * (1 + if) 

it says that when interest rates are higher, its currency depreciates. for long term forecast

Relative economic strength:

An exchange rate forecasting approach that suggests that strong pace of economic growth in a country creates attractive investment opportunities, increasing the demand for the country’s currency and causing it to appreciate. It focus on inverstment flow. It may cover shorter period of currency movement forecast. 

Tobin's q =  MV of companies / replacement value of assets

Equity q = MV of equity/ (MV assets - MV liabilities)

if q < 1, stock is undervalued

Asset Allocation

duration of foreign bond

 adjusted duration = country beta * country duration (don't use correlation here)

 Δprice = adjusted duration * Δyield

contribution to portfolio duration = %weight in portfolio * adjusted duration

new equity                                       current portfolio

sharpe ratio = rp - rf/σf =0.42       sharpe ratio = rp - rf/σf = 0.44

current portfolio correlation with new equity  p*0.44

if  0.42 >  p*044

if greater, should add new equity to portfolio

(favors low correlations)

return of domestic currency 

  Rdc = (1 + Rfc)(1 + Rfx) -1 standard deviation of domestic currency 

 σdc^2 = σfc^2 + σfx^2 + 2 σfcσfx p(fc, fx)

Derivatives

long position in backwardation  - positive roll yield

short position in backwardation  - negative roll yield

long position in contango  - negative roll yield

short position in contango  - positive roll yield

ETF vs futures:
futures are leveraged, and limited lifespan

overall delta of portfolio -> delta is additive

convert a floating rate loan to a fixed rate loan (using pay fixed, receive floating swap)
- increase the market value risk because duration of borrower position goes up, so interest rate sensitivity goes up. When interest rate down , firm is negatively affected.
- but reduce cash flow risk

futures overlay strategy not same as cash market strategy
- futures are on underlying of broad market index, cash market index is not the same as underlying of futures contract. So cash market portfolio could contain non systematic risk.
- equity do not always respond in the precise manner predicted by betas

min variance hedge ratio , h = p(DC,FX)* stddev(DC)/stddev (FX)

repo rate
lowest ------------------------------------------------------------------------------- highest
physical delivery, wire transfer of title, custodial account, no delivery

the more difficult it is to obtain the securities, the lower the repo rate.

roll yield = change in futures price - change in spot price

duration of fixed/floating swap
floating rate = half of its repricing freq
fixed rate = 0.75 of n (maturity)

Put structure do offer some protection if the issuer has an unexpected credit event, such as when put structure is triggered by a credit event --> binary credit put

to gain exposure to an asset class in advance of the cash receipt (pre-investing), take long position in futures on the asset class, no need to invest notional amount by the risk free rate

collar is a cost efficient hedging strategy, hedge downside risk with long put option, offset the cost with short call.

forward conversion with options is a monetization strategy, for concentration position. The goal is borrow against the hedged position and invest the proceeds in a diversified portfolio. It buys put option and short call option at the same strike price, same maturity date, creating a riskless position.

delta hedge
 Nc/Ns = - 1/delta
transaction    dealer's position      hedging transaction
sell puts        long exposure          sell underlying
sell calls       short exposure         buy underlying


Alternative Investments
vintage year bias means over or under weighting in specific vintages. In good years, PE firm shows good return than bad year. So choosing a specific vintage year would create bias.

In hedge fund industry, survivorship bias and backfill bias, the returns are overstated.

Equity
Equitising a market neutral long short portfolio:
client gives you notional to invest you long undervalued stocks, get an alpha. you short overvalued stocks, get another alpha. short the stocks  raises some cash, which you buy equity future and invest in treasuries.

Pairs trading is a market neutral trading strategy that matches long position with short position in a pair of highly correlated instruments.

Equitising Cash:
if you want $100 of stock exposure, buy $100 of stocks, or buy $100 of futures, you still have ($100 - margin required) of cash to earn interest payment (similar to earning a risk free bond)
long stock = long futures + long risk free bonds

CAL, CML difference
all the points on the CAL are combinations of risk free rate and portfolio of risky assets
all the points on the CML are combinations of risk free rate and market portfolio 

market portfolio is the same for everyone
risky portfolio is different for everyone


pooled account (lowest transaction cost), ETF, mutual fund

historical correlation underestimate the volatility of assets class during market crisis contagion

short extension investment style: long positions of 100% + X % , short positions of X %

market neutral funds -> appropriate benchmark is risk free rate, bcoz zero beta, zero systematic risk

indexed portfolios:
full replication: lower tracking risk, automatic rebalancing, high transaction cost
stratified sampling: lower cost to construct, assume return of stocks that are selected are uncorrelated
optimization: accounts for correlation between selected stocks, require continual rebalancing

semiactive management (enhanced indexing):
two forms, derivative based strategy and stock based strategy
stock based strategy: decisions regarding stock holdings are made relative to benchmark weight. If manager has no opinion on the stock, he will hold it in his portfolio at benchmark weight. If negative opinion, underweight it relative to the benchmark weight.If positive opinion, overweight it relative to the benchmark weight.

derivative based strategy: equitise cash portfolio, and alter the duration of the cash.  Use fixed income portfolio and equity exposure through futures market.

- tangency portfolio

corner portfolio with the highest Sharpe ratio

- to find the optimal leverage, combine corner portfolio closest to tangency portfolio, and borrow at risk free, to select a portfolio on the CAL

mismatch in character occurs when gain/losses in concentrated position and offsetting gain/loss in hedge are subject to different tax treatments

  put option - capital gains tax

  stock options - ordinary income tax

Performance Measurement and Trading

Appropriate benchmark help identify whether skill or luck achieve excess return, but they do not reduce the active risk exposures.

Benchmark attributes past performance to security selection or industry bets.

benchmark need not be widely available, eg. custom benchmark

performance attribution is about account performance relative to specific benchmark, not managers past performance.

performance appraisal is about the quality of the account's relative performance , it is investment skill or luck.

total value added return by fund manager (micro attribution)
= weighted average of manager return - weighted average of benchmark return - trading cost

Incremental return of total fund = (total fund value - beginning value - net contribution) / beginning value

macro attributions inputs
- policy allocation ot normal weightings
- benchmark portfolio returns
- fund returns

macro attributions
A : A cash attribution
R - risk free return
A - Asset category return          -- passive indexing return
B - benchmark return                -- style return
I - investment management return    -- active return
A - Allocation effect
transaction cost components
explicit cost: commission
implicit cost: bid-ask spread, market impact cost, missed trade opportunity cost, delay cost

bid-ask spread narrowing -> more liquidity, cost of trading is lower, lower volatility, low risk

return based analysis 
- can be executed quickly, bcoz it is regression
- based on historical data
- use to see overall portfolio behavior
- mutually exclusive, collectively exhaustive, represent distinct sources of risk
- use Shapre style analysis as optimization procedure , portfolio weights must be non negative and sum to one.

holding based analysis 
- can detect style drift quickly bcoz it use recent data
- based on current snapshot of the portfolio
- P/E, dividend yield, EPS growth rate

buy and hold: the investors risk tolerance is positively related to stock market returns -> stock market ↑ , investor's risk tolerance ↑

constant mix: constant risk tolerance , investor desires to hold stocks at all levels of wealth

rebalancing and corridor width
factor                                          corridor width
high transaction cost                     wider
high risk tolerance                         wider
high correlation with portfolio        wider
high volatility of assets                 narrower

Trading tactics
Liquidity at any cost: information motivated traders, timely execution
Cost are not important: market orders, mask trading intention since all market orders lookalike, for small trades and more liquid stocks
Need trustworthy agent: larger order on thinly traded stocks
Advertise to draw liquidity: IPO, secondary offerings, public display the trading interest in advance of the actual order
Low cost whatever the liquidity: limit order

Risk Management
tail VaR: VaR plus the expected loss in excess of VaR
cash flow at risk : CFAR measures the risk to company's cash flow, it is the min cash flow loss that are expected with a given probability over a specified time period
incremental VaR: how adding an asset will affect the overall VaR

methods of estimating VaR
- analytical or variance covariance method: simple, but have normality assumption, not suitable for portfolio that have fat tails, or containing options
- historical method: being non-parametric (no probability distribution assumption), reply on past data
- Monte Carlo method: can use any distribution, generate random outcome given an probability distribution

market risk: left tail risk, risk that value of an asset will go down
credit risk: right tail risk, risk that value of contract increases and counterparty does not pay

GIPS
firm description is required in disclosure
use trade date accounting  (after 1 Jan 2005)
use accrual accounting for fixed income securities
if firm does not use leverage in composite, no disclosure of the use of leverage is needed
annualised three year ex-post std dev of monthly return must be presented for both composite and benchmark (after 1 Jan 2011)
composite description is required in disclosure, such as composite creation date
internal dispersion is required in disclosure
the fee schedule is required in disclosure
currency used to express performance is required in disclosure
the number of accounts in the composite need not be disclosed in advertisement
carve-out must include their own cash balance (after 1 Jan 2010), so cash allocation policy is not needed and would be GIPS compliant (after 1 Jan 2010)
if minimum asset level is set, it must be followed consistently
actual, discretionary, non-fee-paying may be included in at least one composite.
actual, discretionary, fee-paying must be included in at least one composite.
must not link perf of simulated or model potfolios with actual perf
custodial fee is not considered direct trading expenses
portfolio valuations at least monthly (after 1 Jan 2001)
real estate portfolio accounting at least quarterly 
real estate portfolio external valuation at least yearly (after 1 Jan 2012)