FIN 377 Final

Time-Weighted Return

(1 + Period 1 Return) x (1 + Period 2 Return) x (1 + Period 3 Return)

Well-Selected Benchmark Characteristics

(1) Identifiable constituents and weights (2) Prespecified (3) Investable (4) Representative

Individual Investors (Situational Profiling)

(1) Source of Wealth - Employee Stock Participation, Investment Returns, Earned Income, Entrepreneurial Business, Inheritance (2) Measure of Wealth - how wealthy do they consider themselves? (3) Stage of Life - ACSG (4) Personality - cautious and analytical vs. risky trend follower

Differences/Similarities Between DB Plans, DC Plans and Individual Plans

(1) Taxes: DB plans are tax exempt and DC plans are tax-deferred (2) Expenses: Participants pay the investment fees and expenses in a DC plan, whereas the employer pays them for a DB plan. DB plans are not portable if you leave your firm, but DC plan assets can be rolled over into a new employer's DC plan or into an individual retirement account (3) Investment Risk: DB - Sponsor; DC - Employee (4) Funding: DB - Employer; DC - Employee with possible matching from employer (5) Longevity Risk: DB - Sponsor; DC - Employee (6) Investment Decision: DB - Sponsor; DC - Employee from sponsor selected menu

2 Dimensions of Risk Measures

(1) Whether they capture total risk or only so-called systematic risk (2) Whether both upside and downside return variations are considered risk (symmetric measures) or only downside variations are deemed to be risk (asymmetric measures)

Allocation Effect

(Portfolio Allocation (e.g. weight) - Benchmark Allocation) x Return

Interaction Effect

(Portfolio Allocation - Benchmark Allocation) x (Portfolio Return - Benchmark Return)

Selection Effect

(Portfolio Return in Industry/Sub-Section - Benchmark Return in Industry/Sub-Section) x Benchmark Allocation

Net Return

(p(t-1)/p(t)) - 1

Defined Benefit Plans (Definition)

A pool of money set aside by a company, government institution, or union to pay workers a stipend in retirement determined by a pre-specified wage-based formula.

Symmetric Systematic Risk Measure

Beta

Defined Contribution Plans (Definition)

Company can discharge fiduciary obligations by having a plan sponsor maintain a platform with investment options appropriate for the spectrum of employees. QDIA was changed by Pension Protection Act of 2006 to an age appropriate investment vehicle. ( used to be very conservative money market fund). Ability to rollover as opposed to DB.

What happens to DB pension liabilities when corporate bond rates drop?

Corporate bond rates are the discount rate used for discounting liabilities. Therefore, when corporate bond rates drop, pension liabilities increase.

Dollar-Weighted Return

If we invest 100 in period 1, invest 20 in period 2 and take 20 out in period 3, the dollar weighted return would be: $100(1+R)^3 + $20(1+R)^2 - $20(1+R)^1

Why do we use log returns?

If we just use normal returns, then we have a problem of base shift. (i.e. if returns in Taiwan drop 70% one year and then are up by 70%, that does not mean you are back to your starting point because you have a smaller base. You would actually need 233% return to get back where you started). Log returns can simply be added together, but for normal returns you need to have geometric returns (1+R1)*(1+R2)....etc.

Benefits of Asset Allocation

Manages variability, provide for cash flow needs, provides diversification, and generate asset growth (risk-return objectives).

Annualize Mean, Variance, Standard Deviation

Mean & Variance - multiply by 12 Standard Deviation - multiply by square root of 12

Foundations and Endowments (Tax)

Must distribute at least 5% of their assets per annum in order to maintain their tax-advantaged status.

Foundations and Endowments (Return)

Need long-term returns sufficient to cover spending, inflation, and expenses. A baseline required return is given by their long-term target spending or distribution rate plus expected inflation and expenses.

Does a longer horizon mean less risk?

No, the risk is just spread over a longer horizon. The only thing that actually declines is the investor's risk aversion.

Security Market Line (SML)

Relates portfolio expected return to the portfolio's beta

Jensen's Alpha

Return - Expected Return of the Risky Portfolio (just plug in beta of the portfolio). This tells us the alpha that is not due to just risk. E(R) = R(f) + B(R(m) - R(f)) Jensen's Alpha = R(portfolio) - E(R)

Realistic short selling vs. unrealistic short selling

Short selling as a use of funds rather than a source of funds. Removing the long-only constraint may give you negative weights but it is not realistic because you need to account for the margin, the interest on the margin and the return from the short proceeds.

Asymmetric Total Return Measures

Shortfall Risk Value at Risk - minimum dollar loss that should occur with a given frequency or probability over a specified period.

Symmetric Total Risk Measure

Standard Deviation

4 Downside Risk Measures

Standard Deviation Probability of Losing Money Average Loss Value-at-Risk

Foundations and Endowments (Risk)

Tend to have the ability to bear large amounts of risk. Their horizons are long and their obligations are not contractual. Risk tolerance is mitigated if spending is high or if spending must be insulated against portfolio volatility.

Time-Weighted versus Dollar-Weighted

Time-weighted probably show the manager's skill better because they are generally unaware of flows until right before they occur. Dollar-weighted would be a better representation of the actual return the investor achieved.

EMH (Weak, Semi-Strong, Strong)

Weak - prices reflect all market trading information (past stock prices, volume, short interest) Semi-Strong - prices reflect all publicly available information (market trading data, financial statement info, fundamental data about economy and industries) Strong - prices reflect all information.

Continuously Compounded Return Function

ln(p(t)/p(t-1))

James-Stein Estimator

o Adds the assumption that expected returns should be similar across asset classes to the sample data. JS estimator adjusts the sample means toward a common value. o This gives more reliable estimates because it shrinks the most extreme sample means, which are more likely to have been affected by sampling error, toward a central value

Alpha (Definition and its Sources) and Portable Alpha

o Alpha - the average of the logs of the wealth ratio over some period of time. o Alpha sources - absolute return focus (benchmarking problem), information asymmetry (adverse selection, lack of publicly available information), fewer restrictions and constraints (behavioral patterns) o Portable Alpha - separating the allocation of assets among managers from the allocation to asset classes

Mean-Variance Framework (Assumptions)

o Assumptions: investors are risk averse and wealth maximizing, returns are normally distributed, investors are interested only in mean and variance

Portfolio Dispersion

o Dispersion - A measure of the variation in the distribution of returns. It quantifies the concentration of cash flows. You want your asset cash flows as close to the liability horizon as possible to mitigate the risk arising from changes in the slope of the yield curve. o Earlier cash flows will not be reinvested for long, so their accumulated value at the horizon will be relatively insensitive to the reinvestment rate. The value of the remaining, longer cash flows as of the horizon date will not be very sensitive to the rates prevailing at that time

Portfolio Duration

o Duration - the slope of the bond price-yield equation. Duration is a measure of the average maturity of a bond and its sensitivity to parallel shifts in the yield curve. o It can be interpreted as the weighted average of the time until each cash flow will be received with the weights based on the present value of each cash flow. o Longer-maturity bonds have higher duration. Bonds with lower coupons have higher duration. For zero coupon bonds, duration is essentially equal to their maturity. It is at best a rough guide to the interest rate sensitivity of bond prices

Know about changing weights in assets, one sigma out, two sigma out, etc. This was in our last deliverable

o If the target portfolio performs 2 standard deviations away from the market during an isolated year, no rebalancing will be considered as this is determined to be normal market activity, but if the portfolio begins to consistently perform 2 standard deviations from the market, rebalancing will be done. o If the portfolio consistently performs 2 standard deviations from the market, it is likely the portfolio is made up of assets with risk and return characteristics not representative of the agreement with the client. o Even if the portfolio is performing 2 standard deviations better than the market, rebalancing should be considered because when setting the client's portfolio, this performance was not expected and does not represent the agreed upon portfolio management

Immunization

o Immunization - funds the liability at lower cost with minimal risk of falling short due to interest rate movements. To attain a lower cost, the cash-in-advance requirement must be relaxed

Information Ratio

o Information Ratio - ratio of portfolio returns above the returns of a benchmark to the volatility of those returns. Measures a manager's ability to generate excess returns relative to a benchmark and their consistency • IR = (Return of Portfolio - Return of Benchmark) / Standard Deviation of difference between Returns of Portfolio and Returns of Index • IR = (Return of Portfolio - Return of Benchmark) / Tracking Error

Taxes on Corporate/Federal Bonds, Municipal Bonds, Dividend Income, and Capital Gains

o Interest on corporate and federal government bonds is taxes as ordinary income o Interest on municipal bonds is tax-exempt at the federal level. o **The maximum individual tax rate on qualified dividend income has been 15% - the same as the top rate on long-term capital gains. To qualify for the lower rate the dividend must be paid by a US corporation or a qualified foreign corporation and the investor must satisfy a 61-day holding period requirement o Most dividends from REITs are treated as ordinary income o Federal capital gains tax is 15% if the investment is held for more than one year. Investments held for less than one year are taxed at normal income rates o Even investments that don't generate any cash flows are still taxed on an accrual basis (ex: zero-coupon bonds are taxed on the assumed accrued interest)

Mean-Variance Framework (Limitations)

o Limitations to Mean-Variance Framework - not fully customizable, you can't implement intra-period cash flows (like 401k contributions) and non-normal distributions (the fatter tails than reflected in normal distributions) are difficult to include

Liquidity and Capacity

o Liquidity - reflects the ease of trading a particular security or set of securities in different trade sizes o Capacity - the asset level of a strategy that, if exceeded, would lead to an unacceptably low level of realized value added

Differences Between High Yield and Regular Bonds

o Longer-term bonds offer higher yields. High yield (lower-quality) bonds offer a much higher spread than investment grade bonds. o Higher yield bonds have higher default rates

Convexity

o Measures how the slope of the price-yield relationship changes around P. o Convexity is positive if price increase at an increasing rate as the yield declines. Negative convexity implies that price increases more slowly as yield declines. Convexity is positive if duration increases and vice versa

Monte Carlo Simulation

o Monte Carlo Simulation - • This simulation relies on certain inputs such as: current portfolio value, estimates of future contributions to portfolio, annual average return, volatility of the portfolio, withdrawal amounts at retirement • The model then runs a thousand or more outcomes and generally predicts the likelihood of your portfolio lasting a certain number of years.

Mean-Variance Framework

o Popular model for computing optimal asset allocations. It allows you to estimate future market values of wealth and an optimal mix of investments reflecting an investor's trade-off preferences between risk and return o Returns in MV framework are continuously compounded returns (the sum of the returns in each of the underlying periods) o For a given expected return, we can search for the weights associated with the portfolio offering the lowest overall variance - the minimum variance portfolio (MVP), which we can use to plot the efficient frontier o Statistically, historical returns show fatter tails than are suggested by normal distributions

Risk Aversion Coefficient and Relative Risk Aversion

o Risk Aversion Coefficient - the function that trades off mean and variance with a sensitivity parameter. It converts expected returns and variances into a single value o Relative Risk Aversion = - (% change in marginal utility) / (% change in wealth). The higher the RRA, the more risk averse the investor.

Sortino Ratio

o Sortino Ratio - modification of Sharpe ratio that differentiates harmful volatility from general volatility by taking into account the standard deviation of negative asset returns, called downside deviation. A large Sortino ratio indicates there is a low probability of a large loss • Sortino = (Portfolio Return - Target or Required Rate of Return) / Standard Deviation of Negative Asset Returns

Asset Allocation (Definition and 3 Types)

o Term used to describe the set of weights of broad classes of investments within a portfolio o Three types of Asset Allocation • Strategic - set based on long-term goals. They are reviewed and revised at least every 3-5 years Ex: if you're setting your allocation today for the next 30 years • Tactical - responds to short-term changes in investment opportunities. Investors who frequently adjust their exposure to stocks, bonds and cash set their allocations tactically • Dynamic - driven by changes in risk tolerance, typically induced by cumulative performance relative to investment goals or an approaching investment horizon

Market Impact

o The change in transaction costs due to trade volume. It's also described as the price paid for immediate execution compared to patiently waiting for other investors to submit orders. o High-volume, low-volatility securities reflect lower total transaction costs than low-volume, high-volatility issues (larger transaction costs, liquidity is lower)

Defined Benefit Plans (Riskless Investment Plan)

o Timing and magnitude of benefits cannot be known for sure, but payments to retirees for example are highly predictable. Therefore, a customized fixed income portfolio matching the characteristics of the projected benefit payments approximates a riskless investment for the plan

Transaction Costs and Bid-Ask Spread

o Transaction Costs - commissions charged by brokers o Bid-Ask Spread - buy security from market maker at ask price and sell it at bid price. As size of trade grows, bid-ask spread tends to widen

Treynor Ratio

o Treynor Ratio - measures returns earned in excess of that which could have been earned on a riskless investment per each unit of market risk. In theory, the assets with the higher Treynor ratio should be preferred because we can always adjust the absolute level of risk and return borrowing at the risk-free rate • Treynor = (Average Return of Portfolio - Average Return of Risk Free Rate) / Beta of Portfolio

Utility Function

o Utility Function = max (E[U(W)] = maximize expected value of utility of wealth

Asset Liability NVO

o When you essentially know your future liabilities (like in a DB plan), you can treat your plan as a short long-term bond. The liability is added to the portfolio as a constraint with a negative weight because it is effectively a short position. o It looks like the Weight of the Liability = -(liabilities/assets). Be careful interpreting, return is actually the percentage change in the ratio of the plans surplus (assets - liabilities) to its assets, while risk is the variance of these changes

Gross Return

p(t-1)/p(t)

Investment Process

• *Philosophy - Why it should work? When it should work? • *Signal Creation - a fact you can observe early enough to implement an investment bet. Must be significant to dictate a change. • *Capture of Signal - start with model or target portfolio, decide how to construct portfolio and weight each security • Implementation - must factor in transaction costs, trading restrictions, portfolio management procedures that paper portfolios don't include • Feedback - evaluate performance relative to an appropriate benchmark

Individual Investors (Risks)

• Ability to take risk - depends on objective criteria such as investor's wealth relative to needs, investment horizons, life cycle stages, etc. Higher wealth and longer horizon means higher ability to take risk • Willingness to take risk - this is subjective and depends on the investor

Individual Investors (4 Life Cycle Phases)

• Accumulation Phase - individual has a long horizon and growing income, but financial net worth is typically small relative to liabilities and future needs. These individuals can take significant investment risk with funds not allocated to specific short-term goals • Consolidation Phase - the individual's financial net worth is building, and they are earning more than enough to cover current expenses. Their investment horizon begins to shorten, diminishing their ability to take risk • Spending Phase - this phase corresponds to retirement. Others could retire but have not. Individuals are financially independent and expenses can be covered by investment income and assets. This cycle a diminished ability to accept risk • Gifting Phase - when the individuals are confident that their assets exceed their lifetime needs, in which tax-efficient asset transfer and philanthropy become primary considerations

Relationship Between Stocks and Bonds

• Based on average monthly returns, stocks and bonds are positively correlated • Stocks and bonds are positively correlated in "up" markets and weakly negatively correlated in "down" markets • Bonds offer significant diversification potential and they're especially effective when they're needed most, when stocks do poorly

Mean-Variance Framework (Constraints)

• Budget Constraint - portfolio weights sum to 1 • Long-Only Constraint - each asset must have a weight greater than 0 • Shortfall Constraint - limits the probability of earning a return below some threshold level

Individual Investors (Return Requirements)

• Critical goals (maintaining current standards of living and supporting loved ones) give us the required return. • Aspirations (second home, early retirement) give us higher target return.

Defined Benefit Plans (Returns)

• DB plans require a return sufficient to cover projected liabilities in conjunction with planned contributions. This implies a required return approximately equal to a weighted average of the discount rates applied to each future payment in the PBO calculation. • The target return should reflect the built-in growth (implying higher required return) or contraction (lower required return) in measured liabilities

Defined Contribution Plans (Taxes)

• DC plans are tax-deferred at distributions

Defined Benefit Plans (Taxes)

• Defined benefit plans are tax exempt

Defined Benefit Plans (Horizon)

• Depends on whether the plan is expected to terminate or remain a going concern. • Terminating plans have short-term horizons corresponding to the expected termination date. • Ongoing plans have at least two horizons - the first reflects the need to attain fully funded status within 7 years as required by law, the second reflects the presumption that both the sponsor and the plan have infinite lives

Alternative to Mean-Variance Optimization

• Dynamic Programming • In the previous optimizations, we assumed that the future will look like today even though we know it will not. With DP, we can incorporate future opportunities and decisions into our investment strategy. • This is important because recognizing that we may, and probably will, change allocations in the future can help make better decisions. • DP is the "right" thing to do for optimization, but in most cases is very impractical. • You essentially work backwards from the end of your horizon to the present, trying to maximize the portfolio value for the next period

Portfolio Management Process

• Evaluate client characteristics • Assess market opportunities • Define objectives and constraints • Set overall investment strategy, including asset allocation • Select investment managers and specific vehicles • Implement strategy • Measure and evaluate performance • Monitor and adjust

Defined Benefit Plans (Legal and Regulatory)

• Governed by Pension Protection Act of 2006, as well as Prudent Investor Law, state laws, IRS, etc.

What happens if a company freezes or terminates a DB plan?

• If an employer freezes an existing DB plan, the plan continues, but employees accrue no further benefits. The company may need to make further contributions. • If the company terminates the plan, either the accrued benefits, including all unvested benefits, must be paid out as a lump-sum equivalent, or the plan must purchase a annuity. The plan must be fully funded when terminated

Individual Investors (Liquidity)

• Individuals need highly liquid assets sufficient to meet normal living expenses plus an emergency reserve equal to 3-12 months of living expenses

Individual Investors (Horizon)

• Individuals usually have multiple investment horizons corresponding to life cycle stages and specific goals and events. Each horizon should have a different investment strategy

Nominal/Real Returns of Stocks and Bonds

• Inflation - Nominal returns for both stocks and bonds display positive correlation with realized inflation. For stocks, the correlation comes from capital gains and losses. For bonds, the income component of return has a strong positive correlation with inflation while capital gains/loses exhibit negative correlation with inflation • Inflation - Real return on bonds shows a negative correlation with realized inflation. Real stock returns are essentially uncorrelated with realized inflation, meaning stocks are a good hedge against inflation • Real and nominal stock returns are mean reverting over horizons greater than three years. Bond returns seem to trend. This means you should invest more heavily in stocks over long horizons

Defined Benefit Plans (Unique Circumstances)

• It is in the interest of the beneficiaries to limit the correlation between the two primary sources of funding for the plan: the investment portfolio and the profitability and solvency of the sponsor

Defined Contribution Plans (Life Cycle Funds)

• Life Cycle Funds - designed to be more conservative as the investor approaches retirement. • With or without life cycle funds, participants usually adopt the strategy to become progressively more conservative with their portfolios as they approach retirement.

5 Main Categories of Constraints

• Liquidity (any significant payments that must be funded out of the portfolio, recurring needs) • Time horizons (overall horizons, horizons for specific events) • Taxes (taxable vs. tax-exempt bonds, capital gains/losses, etc.) • Legal and Regulatory (trust and estate considerations) • Unique Circumstances (avoiding sin stocks, etc.)

Defined Benefit Plans (Liquidity)

• Liquidity needs depends on the amount of near-term (1-2 years) benefit payments net of expected contributions

Individual Investors (Taxes)

• Major consideration for individuals. Most are subject to federal and state income taxes, but are able to shelter some of their investments via DC plans. Individuals also may be subject to estate taxes

Problems with Passive Management of Bonds

• Managers face problems with passive management of bonds due to the heterogeneity of fixed-income instruments, time-varying risk characteristics, and the virtual absence of a secondary market for many issues included in standard fixed-income benchmarks • Few bond issues trade actively and today's liquid new issue will be tomorrow's illiquid legacy, so bond index managers do not have the luxury of picking bonds randomly or eschewing illiquid instruments

Example Objective Functions

• Maximize portfolio return minus lambda * variance of portfolio (max/min problem) • Tangent Portfolio - maximize Sharpe ratio (the extra expected return per unit of risk we get for investing in stocks rather than in the riskless asset) • Minimize variance of portfolio. Constraints: long-only, sum of weights=1, etc.

Performance Attribution (Returns-Based vs. Holdings-Based)

• Performance Attribution - attempts to identify the source of portfolio returns. This is an attempt to identify the risk factors that best explain performance, and by inference, the impact on performance of the manager's investment decisions. • Returns-based attribution is a top-down approach that requires only returns data for the portfolio and for asset class indexes. • Holdings-based attribution requires the history of security level holdings for both the portfolio and the benchmark index as well as returns data for all the securities in the portfolio/benchmark

Example Active Equity Strategy

• Philosophy - invest in value stocks, stocks with low P/B's since we're coming out of poor economic times • Signal Creation - calculate P/B using forward earnings estimates • Capture of Signal - rank stocks on P/B within each sector (energy, consumer staples, healthcare), buy lowest 1/3 • Implementation - rebalance quarterly • Feedback - review performance of low P/B stocks in general, our 1/3 list, then our portfolio

Defined Benefit Plans (PBOs and ABOs)

• Projected Benefit Obligation (PBO) - value of benefits expected. It's more difficult to calculate than ABO. IT includes the expected increases in future wages and expected future vesting patterns. Given generally rising wages, the PBO often exceeds the ABO by a substantial margin • Accumulated Benefit Obligation (ABO) - Value of total benefits accrued thus far. It reflects the obligation the sponsor could lock in by terminating the plan today

Investment Policy Statement (Purpose and Sections)

• Purpose - To summarize key information about the client and the investment strategy so that any competent investment professional can readily implement the plan • Sections:  Description of Client - life stage? Horizon?  Purpose of the IPS - set expectations  Duties of the Parties  Objectives  Constrains  Asset Allocation Targets  Guidelines for Portfolio Adjustment and Rebalancing  Schedule for Portfolio and IPS Reviews

Defined Benefit Plans (Risks)

• Risk is relative. Risk should be assessed in terms of the plan's surplus/deficit of assets vs. liabilities, rather than the asset portfolio alone. • The plan's ability to bear risk depends on the surplus, the size of the plan relative to the sponsor's business, the health of the sponsor, and the demographics of the workforce.

Sharpe Ratio

• Sharpe Ratio - measures risk-adjusted performance of portfolio. Higher the Sharpe ratio the better • Sharpe = (Expected Portfolio Return - Risk Free Rate) / Portfolio Standard Deviation

Individual Investors (Unique Circumstances)

• Significant contingent obligations like supporting an ill family member, concentrated positions in illiquid equities like a family business, etc.

Defined Contribution Plans (Legal and Regulatory)

• Subject to same standard as DB plans with Pension Protection Act.

Passive Management of Bonds

• To create a portfolio that tracks an index closely without frequent/costly rebalancing, a manager must match the structure of the index across several dimensions - maturities, coupons, credit qualities, sectors, individual credit exposures - in addition to the broad requirement of matching the index's duration. They are not "static" portfolios - they require ongoing management • The manager must match the contribution to duration - the portfolio weight times duration - of the holdings in each category (ex: sector) to that of the index

3 Categories of Risk

• Volatility - deviations, positive or negative, from the expected outcome. It is generally associated with the standard deviation or variance • Downside Risk - the probability that your return will fall below some threshold return. Downside risk measures are generally not proportional to the investment horizon. Examples of downside risk measures: probability of losing money, average loss, value-at-risk (VaR - 95% confidence lower bound - the threshold where there is only a 5% chance of a lower return) • Tracking Error - standard deviation of return differentials, indicates how closely a portfolio tracks the benchmark