Performance Measurement

Sharpe Ratio: The Sharpe ratio tells us whether a portfolio's returns are due to smart investment decisions or a result of excess risk. This measurement is very useful because although one portfolio or fund can reap higher returns than its peers, it is only a good investment if those higher returns do not come with too much additional risk.

(Return onPortfolio−Risk Free Rate)STDof Portfolio

Explain why the sharpe ratio is not an appropriate performance measure for individual managers and calculate whether a new manger should be added to a portfolio Most of the deviation in return will be attributable to the benchmark. The IR is a better measure as it is relative to the benchmark. Sharpe is reliable whether or not to add a fund to an existing portfolio. The sharp must be higher than the portfolio’s.

Treynor’s Measure: In other words, the Treynor ratio is a risk-adjusted measure of return based on systematic risk. It is similar to the Sharpe ratio, with the difference being that the Treynor ratio uses beta as the measurement of volatility.

(Return onPortfolio−Risk Free Rate)Portfolio Beta

Jenson’s Measure: A risk-adjusted performance measure that represents the average return on a portfolio over and above that predicted by the capital asset pricing model (CAPM), given the portfolio's beta and the average market return.

Returnon Portfolio−CAPM

Information Ratio: A ratio of portfolio returns above the returns of a benchmark (usually an index) to the volatility of those returns. The information ratio (IR) measures a portfolio manager's ability to generate excess returns relative to a benchmark, but also attempts to identify the consistency of the investor.

(Return onPortfolio−Risk Free Rate)Tracking Error

R-Squared : A statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For fixed-income securities, the benchmark is the T-bill. For equities, the benchmark is the S&P 500

R^2 = 1−σ2(e)σ2

Up-capture Ratio: A statistical measure of an investment manager's overall performance in up-markets. The up-market capture ratio is used to evaluate how well an investment manager performed relative to an index during periods when that index has risen. The ratio is calculated by dividing the manager's returns by the returns of the index during the up-market, and multiplying that factor by 100. For example, a manager with an up-market capture ratio of 120 indicates that the manager outperformed the market by 20% during the specified period.

Down-Capture Ratio : A statistical measure of an investment manager's overall performance in down-markets. The down-market capture ratio is used to evaluate how well or poorly an investment manager performed relative to an index during periods when that index has dropped. The ratio is calculated by dividing the manager's returns by the returns of the index during the down-market and multiplying that factor by 100. For example, a manager with a down-market capture ratio of 80 indicates that the manager's portfolio declined only 80% as much as the index during the period in question.

T-Value: (Estimated Value) / (Standard Error Value)

If t > 0 value cannot be 0If t < 0 value can be 0

Risk: Style Drift Interpret the results of an equity style box analysis and discuss the consequences of style drift

Style boxo Used to characterize mutual funds and stocks (large, small, mid, value, growth, core)o Style drift = strays from original state style objective

Base for investor = 1) will not receive desired style exposure 2) Manager will be moving out of an area of her expertise

Holding based is better at looking at style analysis

Style BoxLargeMediu

mSmall

Value Blend Growth

Portfolio Risk Measurement

Standard Deviation: a value calculated to indicate the extent of deviation for a group.

Skew: a measure of a distribution’s asymmetry. In a positive skew, the standard deviation overestimates risk. Conversely when a distribution is negatively skewed it underestimates risk.

Skew=E [r (s )−E (r ) ]3

σ3

Kurtosis: is a measure of the degree of fat tails. When fatter tails are present the standard deviation will underestimate the likelihood of extreme events.

E [r ( s )−E (r ) ]4

σ 4−3

Utility Function (Risk neutral coefficient = 0)

U=E(r )– .005 Aσ 2

Portfolios of One Risky Asset and One Risk-Free Asset

Expected Return of Complete Portfolio = Risk Free Rate + Proportion of investment budget allocated to risky asset * Risk Premium

E(r¿¿c)=R f+ y ¿¿

Standard Deviation of Complete Portfolio = Proportion invested in risky asset * standard deviation of risk asset

σ c= y∗(σ p)

Capital Allocation Line (CAL): A line representing all possible combinations of risky and risk-free assets. Also known as the "reward-to-variability ratio"

Slope of the CAL = Risk Premium/ Standard Deviation of Risky Asset

E(r¿¿ p)−R fσ p

¿

Diversification and Portfolio Risk

Market Risk/Systemic Risk/Non-diversifiable Risk: Risk associated with the general markets and which are cannot be eliminated through diversification.

Unique Risk/Firm-Specific Risk/Non-systematic Risk/Diversifiable Risk: Risk associated with specific securities and which can be eliminated through diversification.

Portfolios of Two Risky Assets

Covariance = SB

Expected Return on Portfolio = Weight of X * Expected Return of X + Weight of Y * Expected Return of Y

E(r¿¿ p)=wD E(r¿¿D)+wE E(r¿¿E)¿¿¿

Variance of Portfolio = Weight of X * Variance of X + Weight of Y * Variance of Y + 2 * Weight X * Weight Y * Covariance of X and Y

σ p2=wE

2 σ D2 +wE

2 σ E2 +2wDwECOV (¿rd,ℜ)¿

To Minimize the Standard Deviation

1) Find the weight D: σ E2−Cov (rd ,ℜ)

σ E2 +σ D

2−2COV (rd,ℜ)

2) Find Weight E: 1 – Weight D3) Plug in weights into portfolio variance formula

Summary: Although the expected rate of return of any portfolio is simply the weighted average of the asset expected return, this is not true of the portfolio’s standard deviation. Potential benefits from diversification arise when correlation is less than perfectly positive. The lower the correlation coefficient, the greater the potential benefit of diversification. In the extreme case of perfect negative correlation, we have a perfect hedging opportunity and can construct a zero-variance portfolio.

Asset Allocation with Stocks, Bonds, and T-Bills

The Capital Allocation Line which lies tangent on the opportunity set yields the optimal risky portfolio

Utilizing both the lessons learned from investing in a portfolio with a risky asset and risk free asset, and a portfolio with two risky assets we can find the optimal risky portfolio.

Finding the Optimal Risky Portfolio/Maximize the slope of the CAL

a) Find Weight D: Weight D = (E¿¿ (rd )−r f )σE

2−(E( ℜ)−rf )∗COV (rd ,ℜ)

(E¿¿ (rd )−r f )σ E2+(E( ℜ)−rf )σD

2 −¿¿¿¿

b) Find Weight E: 1 – Weight Dc) Plug in weights into the reward – variance slope equation using returns and standard

deviation from the portfolio with two risky assets

Arriving at the optimal Complete Portfolio

1) Specify the exact values used for the variables (expected return, standard deviation, covariance)2) Find the optimal Risky Portfolio

a) Use the following Equation to find the weights

Find Weight D: Weight D = (E¿¿ (rd )−r f )σE

2−(E( ℜ)−rf )∗COV (rd ,ℜ)

(E¿¿ (rd )−r f )σ E2+(E( ℜ )−r f )σ D

2−¿¿¿¿

Find Weight E: 1 – Weight Db) Find the expected return and standard deviation using the formulas from a portfolio with

two risky assetsE(r¿¿ p)=wD E(r¿¿D)+wE E(r¿¿ E)¿ ¿¿

σ p2=wE

2 σ D2 +wE

2 σ E2 +2wDwECOV (¿rd,ℜ)¿

c) Plug in the values into the reward-variance slope formula. THIS YIELDS “Y” which is the percentage that should be invested in the risky portfolio the rest goes into the risk free asset

E(r¿¿ p)−R fσ p

¿

When two assets are perfectly negatively correlated, you can use the following formula to find the weights of each (set the standard deviation to 0):

The Markowitz Portfolio Selection Model

To calculate the optimal portfolio you need the expected return, variance, covariance and the weight of each security.

Portfolio Variance:

1nσ 2+ n−1

nCOV

β i=Cov(r i , rm)

σM2

Portfolio Management

Passive Investing

a) Index Investing

Mutual Funds vs. ETFs

1) Management expenses are higher for mutual funds2) Brokerage commissions are higher for ETFs3) Overall ETFs are cheaper than mutual funds

Separate vs. Pooled Accounts

1) Pooled funds are better for smaller funds which don’t merit individual attention2) Difficult to separate performance in a pooled fund3) Manager will likely have to maintain high levels of excess cash to maintain a pooled fund

Approaches to Creating an Indexed Portfolio

Name Advantage MethodFull Replication Low Tracking Error Replicate the stock weights in a

given indexStratified Sampling Do not have to purchase all the

stocks in the indexSeparate the index into three chosen categories and select a few stocks to represent each category

Optimization Leads to a relatively low tracking error

Matches the fund`s factor risk with that of the index

b) Long Short Strategies (Market Neutral) - Use the risk free rate at the benchmark

Extension Strategies (130/30)

- Allows the investor to have some shorting availability- Use of leverage to compound returns

Fee Schedules:

- Asset based (ad valorem) - Performance based (incentives should be symmetric: penalties for underperformance and

rewards for outperformance, aligns the manager’s interests with that of the client)

Hedge Fund vs. Mutual Funds Describe the major characteristics of hedge funds and contrast them with mutual funds

1) Hedge funds are private investment vehicles for qualified investors2) Hedge fund portfolios are more concentrated3) Use of derivatives4) Hedge funds may take long or short positions5) Leverage6) Use of non-public securities

Future TrendsDescribe the four business models that are likely to be available to asset managers in the future

Firms that provide beta focused products: Experts in cost reductions and will focus on investment process. Low cost but high AUM. Growth opportunities will come from bespoke beta.Firms that provide alpha focused: Limited AUM but larger fees. Ex. Hedge funds, private equity, commodity trading, real estate, distressed debt.Firms that provide investment solutions: Asset allocation, portfolio construction, manager searchesFirms that provide a collection of investment products: (Multi-boutiques): Limited capacity for AUM but high fees. Hedge funds, private equities and real estate = examples.

Beta Drivers vs. Alpha Drivers Explain and identify beta drivers and alpha drivers as investment products

Beta Drivers: Exposures to market risk factorsAlpha Drivers: Exposures to active return factors (active management) Alternative assets are commonly alpha drivers.Managed mutual funds = beta drivers

List of Alpha Drivers: Long/short investments: Market neutral, non-zero betaAbsolute Return Investments: Not constrained to benchmark and able to seek alpha (More leeway then long/short)

Segmented Markets: Areas where people don’t normally invest aka commodities / distressed debtPortfolio Concentration: Large bets on few securitiesNonlinear return distributions: Option like payoffsAlternative beta exposures (cheap beta): Expanding systematic risk exposures beyond stock/bond. Currency / commodities = examplesThe risk / return increases in that order as well (Page 88) Beta è Alpha

Risk Mitigation

Hedging Strategies

Options Futures Forwards Swaps

http://www.investopedia.com/slide-show/options-strategies/

(Know slides 2, 4, 5, 7, 9)

Drawbacks of Using Futures as Opposed to Forwards

i. The contract size is fixed and is unlikely to exactly match the position to be hedged

ii. The expiration dates of the futures contract rarely match those for the currency inflows/outflows that the contract is meant to hedge

iii. The choice of underlying assets in the futures markets is limited, and the currency one wishes to hedge may not have a futures contract

Types of Imperfect Hedges

a) Cross Hedges: when currencies don’t matchb) Delta Hedges: when maturities don’t matchc) Cross & Delta Hedges: when both currencies and maturities don’t match

Advantages of Using Swaps, Low Default Risk:

- Right of Offset Clause- Companies are screened and those who are small must post initial margin- Credit Trigger Clause: stating that if the customer’s credit rating is revised downward, the

financial institution can terminate the swap and settle for the swap’s market value at the moment.

Option Greeks:

Delta: The ratio comparing the change in the price of the underlying asset to the corresponding change in the price of a derivative. Sometimes referred to as the "hedge ratio."

Gamma : The rate of change for delta with respect to the underlying asset's price. Gamma is an important measure of the convexity of a derivative's value, in relation to the underlying.

Change∈DeltaChange∈the priceof theunderlying asset

Theta: A measure of the rate of decline in the value of an option due to the passage of a day. Theta can also be referred to as the time decay on the value of an option. For example, if the strike price of an option is $1,150 and theta is 53.80, then in theory the value of the option will drop $53.80 per day.

Vega : The measurement of an option's sensitivity to changes in the volatility of the underlying asset. Vega represents the amount that an option contract's price changes in reaction to a 1% change in the volatility of the underlying asset.

Rho: How much does the value of the option change in response to changes in the domestic interest rate

Rho*: How much does the value of the option change in response to changes in the foreign interest rate

Call PutPrice Increases + -Strike Price Increases - +Interest Rate + -Foreign Interest Rate - +Time + +Volatility + +

Put Call Parity: http://en.wikipedia.org/wiki/Put%E2%80%93call_parity

Diversification Techniques

- Exchange funds: several individuals combine their large, low basis holdings in a single portfolio. Usually however investors must stay in the fund for a minimum of 7 years

- Hedging

Investment Policy

Creating an IPS

Five Major Constraints

1) Time Horizon2) Tax Considerations3) Liquidity4) Legal and Regulatory Factors5) Unique Circumstances

Examples

Asset Allocation

Attribution:

Pension Plans

Ethics

Misc Links: http://www.theglobeandmail.com/report-on-business/canadian-crude-prices-see-strong-start-to-2014/article16335942/