The Experts In Actuarial Career Advancement. Product Preview. For More Information: or call 1(800)

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1 P U B L I C A T I O N S The Experts In Actuarial Career Advancement Product Preview For More Information: Support@ActexMadRiver.com or call 1(800)

2 OBJ1-1 MODERN INVESTMENT MANAGEMENT (LITTERMAN) CH 2 - THE INSIGHTS OF MODERN PORTFOLIO THEORY I. THE ADVERT OF FINANICAL ECONOMICS (FE) 1. Axiom: More risk, more return 2. Risk a) quantifies the probability and size of loss. A loss => postponed/ no consumption b) Loss is a random event c) may generate loss => impact net worth => reduce risk appetite in the future => limited future growth, and reduced risk appetite d) is a scarce resource 3. A Investment process helps investor prepare for assuming risks 4. Investors have limited risk appetite => needed to budget it wisely a) Goal: max return per unit of risk (Micro-economics) i) => same utility per dollar spent on every purchase ii) => same return per unit of portfolio risk iii) If (return/risk)a > (return/risk)b, then invest (return/risk)a and drive down (return/risk)a until they equalize 5. Basics a) E(T) = E(T1) + E(T2) E(Tn), linear relationship b) Return can be compounded c) Var(X + Y) = Var(X) + Var(Y) 2Cov(X,Y), risk holds non-linear relationship i) Play around the correlation term to lower the risk through diversification d) Diversification can either i) Increase the return given the same level of risk ii) Or decrease the overall portfolio risk e) Loosely speaking, assets roughly independent, risk compounds ~ sqrt (Time), while expected returns is linear over time i) Assume 0.01% of risk generates 0.02% of return per day. ii) Take 0.01% risk a day over a long term (e.g. 1 yr) => sqrt(252 trading days * 0.01%) ~ 16%/yr =>252 days *0.02% ~ 5% return/yr iii) However, take 16% in ONE day, generates 0.02%*16 = 0.32% of expected return (simple proportion), this is the math for long term investors 6. Modern Portfolio Theory a) Insight through the size, control the expected return of targeted asset in relation to the impact on the risk of the total portfolio b) Hard to quality return and variance (historical/ forward-looking definition, etc) c) Focus on the correlation among assets, how one value move up and down relate to others d) Avoid concentration of risk => diversification => look at overall risk profile! i) Quantify how much a risk budget that an investment should consume e) An application. A business owner sells his business, obtain proceeds, and park in money market fund for a long time before making further decision

3 OBJ1-2 i) Bad idea too much wealth in unproductive fund (negative real return after tax) too long ii) better fully diversify the proceeds and earn a better return f) Process of helping your client i) Identify risk tolerance ii) Experience reveals that the client s risk appetite swings from the extreme risky (business) to virtually riskless (money market fund), clients go to either extreme, seldom in between. Avoid this situation. g) A good investment decision and a good investment outcome do not necessarily have a cause-and-effect relationship. A good outcome is due to luck in short term. h) Risk management framework i) Identify the sources of risk ii) Deploy risk effectively max Ri, Ri =(return i / unit of portfolio risk), i = ith assets. How to measure risk? Many definitions, e.g., volatility, mean-absolute deviation, etc... iii) Find out your risk tolerance => fix the risk you accept, then max return. If risk budget isn t fixed, you can always increase return by adding risks. iv) Adjust the size, then improve returns, control the risk v) Building blocks - diversifier asset relatively independent of others, risky by itself, little risk to the overall portfolio vi) People ask how to invest?? Proper thinking should be measuring and monitoring the universe of assets, how much to invest to improve return and reduce overall risk. vii) Good stuff are => add less risk to the portfolio => use up less risk budget => buy more! (Heuristic meaning of the mathematics of the portfolio theory) i) Process of optimizing portfolio i) Identify all assets in your universe ii) Determine portfolio risk tolerance, fix risk budget iii) Recall, Ri =(return i / unit of portfolio risk), i = ith assets. iv) Buy and sell asset such that R1 = R2 = R3 =... Rn, n = nth assets! v) Domestic / International index fund example vi) Buy and sell such that R(domestic) = R(international). If R(domestic) > R(international), then short R(international), buy R(domestic) until the equation holds, and vice versa. vii) Apply the two-asset scenario to n-asset scenario II. QUESTIONS 1. Given you have n classes of assets, describe a process of constructing an ideal portfolio? Define what an ideal portfolio is, what modern portfolio theory say when managing your portfolio. 2. What is the purpose of diversification?

4 OBJ1-3 MODERN INVESTMENT MANAGEMENT (LITTERMAN) CH 2 - THE INSIGHTS OF MODERN PORTFOLIO THEORY (QUANTITATIVE QUESTIONS) I. LITTERMAN, CH02 1. Imagine you view a portfolio frontier, you either max the return given a fixed level of risk, or min the portfolio risk given a fixed level of return. 2. Two-asset case (domestic index, international index) 3. Let d and f = weights of domestic and international index funds respectively 4. ρ = correlation between domestic and international index 5. Mathematics a) Portfolio risk (d, f) = (d 2 *σ 2 d + f 2 *σ 2 d + 2*d*f*σ d *σ f *ρ) 1/2 (1) b) Marginal contribution to portfolio risk of domestic equities i) Δ d (δ) = ( Risk (d + δ, f) Risk (d,f) ) / δ (2) c) Similarly, i) Δ f (δ) = ( Risk (d, f + δ) Risk (d,f) ) / δ (3) d) Goal: decide 10% of portfolio risk (fix the risk budget), then max the expected return i σ i Expected excess return i Total Return d 15% 5.5% 10.5% f 16% 5.0% 10.0% Cash 0% 0.0% 5.0% e) ρ = 0.7, domestic and international correlates! f) Goal: make sure (e d / Δ d ) = (e f / Δ f ),..(*), if imbalance, short low and buy high to equalize g) Initially, 100% domestic index, now, we need to optimize the total portfolio h) Since the goal is 10% risk, and we have 100% domestic fund, we need to sell some domestic fund, because σ d =15% > 10% (our target) i) Intuitively, 2/3 to domestic, 1/3 to cash, => 10% portfolio risk, can we do better? j) Differentiate (1) w.r.t. d and f, we get i) Δ d = d*σ 2 d + f*σ d *σ f *ρ / Risk (d,f) (4) ii) Δ f = f*σ 2 f + d*σ d *σ f *ρ / Risk (d,f) (5) k) When f = 0, => no international equity i) (4) Δ d = ( d*σ 2 d ) / (d*σ 2 d ) 1/2 = σ d = 0.15 ii) (5) Δ f = ( d*σ d * σ f * ρ ) / (d 2 *σ 2 d ) 1/2 = ρ * σ d = l) Suppose the portfolio has infinitely many unit, ν, and you want to sell one unit of domestic equity, i.e. δ = -1, i) The portfolio risk is decreased by Risk(d + δ, f) Risk(d, f) = 0.15*δ = ii) To maintain (*) in equilibrium, the investor must purchase (Δ d /Δ f ) = 0.15/0.104 = unit of international index m) unit of international index increases the expected return by (1.442)*(0.5) = , selling one unit of domestic index reduce the expected return by (1)*(5.5%) = -5.5%. In summary, the net increase in return is The benefit is clear, and the investor should short domestic fund until (*) holds

5 OBJ Hurdle rate, the indifferent rate of return on international index, an implied view of the portfolio a) Trick: define the expected excess return, not expected return b) Considering: 1.442*e f +(-1)*(0.055) = 0 => e f = 3.8% c) Implication: If expected return on international equity < 3.8% => won t consider 7. Short domestic and long international until (*) holds equilibrium. Purchase an asset A if the expected excess return on A > the hurdle rate, and short if the expected excess return on A < the hurdle rate. 8. Case asset example: the new asset = commodity, (σ 2 = 25%; ρ with domestic = ρ with international = -0.25) is good, because it can reduce portfolio risk, commodity is a good diversifier. 10. Applying the same analysis, optimal weight of commodity = 10% to min the portfolio. 11. Holding fixed weights in all other assets, there is a risk-minimizing position for each asset. Weights greater than that risk-minimizing position reflects your positive implied views; weights less than that risk-minimizing position reflect bearish views. 12. If you optimize your portfolio, look for assets that produce positive expected excess return, and that are uncorrelated with the portfolio. Inclusion of these assets is beneficial. 13. Case 3 a) Suppose an asset that has some correlation with the existing portfolio => there is a non-zero risk-minimizing position => any position between zero and that riskminimizing position is an opportunity for investors. 14. By modern portfolio theory, shop for assets that have negative or low correlation of the portfolio, and that has an expected excess return, identify a risk-minimizing position, inclusion of it is usually beneficial. II. QUESTIONS 1. Concept question. A client approaches you, an investment actuary, and asks, I have an asset from Mars, which gives me an expected excess return, and has no correlation with the existing portfolio, should I buy some? How much should I buy? Can you teach me? 2. Make sure you know how to calculate the optimal weight of the two-asset example.

6 OBJ1-5 MODERN INVESTMENT MANAGEMENT (LITTERMAN) CH 17. RISK MONITORING & PERFORMANCE MEASUREMENT I. 3 LEGS OF FINANCIAL CONTROL 1. Risk Plan (5 guideposts) a) Set expected return and volatility (VaR and tracking error) goals i) Scenario analysis to identify factors of failure b) Define points of success and failure (ROE / RORC) i) Risk capital defined with VaR methods c) Show how risk capital will be deplored to meet objectives i) Define min. acceptable RORC for each allocation ii) Explore correlations to ensure ROE and variability acceptable d) Set Bright Line defining events that inflict serious damage from disappointing ones i) Indentify which one needs insurance coverage e) Identify critical internal and external dependences (in good and bad environ.) i) Describe response nature if dependences breakdown 2. Risk Budget (asset allocation) Quantify risk plan a) Aggregate expectation of each allocation consistent with organization s obj. and tolerances b) Management must define time horizon of risk budget and for RORC measurement c) Example: Investment portfolio impact on earnings volatility on reported earnings i) From business and risk plan, identify acceptable RORC and ROE over different time frames ii) Determine appropriate weights for each investment class iii) Simulation and sensitivity testing iv) Ensure appropriate individual and aggregate risk level as per planning v) Ensure acceptable volatility around expected return vi) For each significant downside scenario, devise contingency steps bring logical and measured response 3. Risk Monitoring Principal concern if investment activities are behaving as expected 4. II. INDEPENDENT RISK MANAGEMENT UNITS 1. Objectives a) Gathers, monitors, analyze and distribute risk data to right people at right time i) Develop (a) disciplined process and framework to identify and address risk topics; (b) risk data inventory; (c) risk measurement and performance attribution tool ii) Promote (a) risk culture and internal control environment; (b) transparency of risk info. iii) Set and implement risk agenda; Identify trend before becomes a big problem iv) Catalyst for comprehensive discussion of risk-related matters v) Should not manager risk (responsibility of individual portfolio manager)

7 OBJ Permit users to be conclusive a) If forecasted tracking error consistent with target? i) Compare Forecast tracking error with tracking error budget for reasonableness ii) Policy to set the magnitude of variance from target as unusual b) If risk capital spent in the expected themes for each portfolio? i) If not in line, may indicate style drift by individual manager ii) Monitor risk decompositions of acceptable active weights and marginal contribution to risk at stock, industry, sector and country level c) If risk forecasting model is behaving as expected (explore tracking error stresses) i) Techniques - Simulation (short fall: observed history only gives 1 set of realized outcomes) / Monte Carlo simulation (more robust) 3. Quantifying Illiquidity Concerns a) Dramatic change in Liquidity profile during hard times b) Some illiquid situations (e.g. 144A securities, position concentration) can coincide with unanticipated capital redemption - Risk often apparent only if large stresses are assumed 4. Credit Risk Monitoring - Ensure all counterparties meet credit policy criteria III. PERFORMANCE MEASUREMENT TOOLS AND THEORY 1. Objectives a) Determine if manger generates i) Consistent excess risk-adjusted performance over benchmark ii) Superior risk-adjusted performance over peer iii) Sufficient return for risk assumed (cost/benefit) b) Identify such manager 2. Why use multiple Performance measurement tool a) Most comprehensive measurement - Risk has many human dimensions b) For very different results from different tools, risk profession to apply judgment 3. Improve meaningfulness of Performance Measurement Tools a) Must supplement tools with i) Clear articulation of management philosophy from individual manager ii) Routine position and style monitoring process (early warning system) b) Tools: Attribution of returns / Sharpe and Information ratios / Alpha vs. benchmark and peers

8 OBJ2-54 Mr. Robert North. I. INTRODUCTION 1. Authors are strong are their suggested approach to measuring assets and liabilities 2. Where the authors could do more is to address the implications of the FE approach on: a) Funding Policy i) Contribution patterns ii) Intergenerational equity b) Investment Policy i) How much risk is appropriate? ii) Why not take the risk if it is manageable c) Benefit Policy i) What level and type of benefits should be provided? ii) Would negotiating parties accept not getting benefit of advance risk recognition? d) Accounting/Expense Policy i) At what rate should pension liabilities be recognized? benefit accrual rates are usually uniform in pension plans ii) Will accounting rules drive behavior rather than measure it? 3. Mr. North agrees with authors approach to measuring liabilities a) But not clear that this should result in changes to funding policy, investment policy and/or benefit policy ******************************. AUTHORS RESPONSE TO ISSUES RAISED BY MESSRS. ZVI BODIE, JOHN RALFE, AND ROBERT NORTH I. SUMMARY 1. Remember that the plan sponsor should not be regarded as a separate entity from shareholders or taxpayers 2. The principals should want to see the true cost, although the agents may want to understate cost of benefit improvements 3. Regarding accounting rules driving policies, authors note that this is happening in the current environment a) Believe that better information will produce better policies

9 OBJ2-55 II. CONCLUSION 1. Authors have deliberately chosen a narrow focus that of liability measurement 2. Three critical insights a) Incorrect to attribute to the plan sponsor financial interests such as the ability to bear risk or entitlement to rewards i) These belong only to the taxpayers/shareholders who bear the risk b) Liabilities are measured without regard to the expected return on risky assets that may be used to fund these liabilities c) Outside the actuarial profession, vast majority of thought leaders in the financial community agree with (a) and (b)

10 OBJ2-56 ACCOUNTING FOR PENSION BUY-IN ARRANGEMENT IRM I. DEFINITION OF BUY-IN 1. Company still responsible for paying bfts but purchases a contract from insurer 2. Designed to provide returns equal to all future bft payments to covered participants a) Zero net ongoing cash outflow to participants (i.e. bfts entirely funded by buy-in contract) 3. No settlement accounting but has certain advantages of annuity purchase 4. Note: Under buy-out, plan transfer responsibility for future payment to insurer triggers settlement accounting II. BACKGROUND 1. Structure of buy-in contract a) May cover some or all of existing pension obligations b) Single premium arrangement, similarly priced as for buy-out contract c) Allow conversion to buy-out contact at no extra cost 2. Accounting for a Buy-In Arrangement a) Doesn t qualify for settlement accounting (Primary responsibility still rests with the sponsor e.g. If insurer cannot pay) b) It is an investment contract (plan asset at fair value) III. DETERMINATION OF FAIR VALUE OF BUY-IN CONTRACT 1. Approach #1: Measure at plan measurement date a) Initial measurement Purchase price b) Subsequent measurement Estimated exit price (i.e. selling contract to a 3 rd party) i) Similar considerations used by insurer when pricing the contract ii) Current discount rate 2. Approach #2: Used stated cash surrender value as fair value proxy a) Short-coming: cash out formula may have hefty termination provision IV. ONGOING ACCOUNTING FOR PBO ANY ADJUSTMENTS FOR PBO NEEDED? 1. Approach #1: Continue with ER's traditional discount rate and mortality assumptions 2. Approach #2: PBO = FV of buy-in contact at measurement date (Also consider changing mortality assumptions) 3. Need to recognize actuarial loss at next measurement date given PBO is increased to match higher contract purchase price. (After the 1 st measurement date, PBO and FV should be equal)

11 OBJ2-57 Buy-in contract Buy-out annuity Balance Sheet Current I/S Future I/S No change; contact is asset Remove obligation and related assets No settlement GL Settlement GL Status quo No change No settlement GL Continue amortization in AOCI; less volatile expense No future AOCI amortization, no expense volatility Continue AOCI amortization and EROA assumption

Expected Return Methodologies in Morningstar Direct Asset Allocation

Expected Return Methodologies in Morningstar Direct Asset Allocation I. Introduction to expected return II. The short version III. Detailed methodologies 1. Building Blocks methodology i. Methodology ii.