Asset Allocation

Describe the framework for developing CME

1: Define asset classes and horizon. 2: Research historical record. 3: Specify models. 4: Determine info sources. 5: Interpret. 6: Document conclusions. 7: Monitor outcomes

Define cross-sectional consistency and intertemporal consistency

Cross-sectional is consistency across asset classes regarding risk/return characteristics. Intertemporal is over investment horizons.

Define rebasement

specific period used as the base of an index is changed

Errors in data series

transcription errors, survivorship bias, and smoothing.

Define asynchronous data

Samples from different time periods even labeled the same (diff time zones)

How does increasing data frequency help with accuracy of estimates?

Helps with variance/covariance but not mean (requires longer history of data)

time-period bias

Research findings often turn out to be sensitive to the selection of specific starting and/or

ending dates.

Conditioning information

Separate recession and expansion betas and returns when calculating expected return

Peso problem

The peso problem is when a feared disaster doesn't occur, leaving realized returns that look high and safe but actually overstate true expected returns and understate true risk.

The four possible causes of correlation are

1) A predicts B, (2) B predicts A, (3)a third variable C predicts both A and B, or (4) the relationship is spurious.

Prudence bias

the tendency to temper forecasts so that they do not appear extreme or the tendency to be overly cautious in forecasting.

The three uncertainties analysts encounter are:

model uncertainty, parameter uncertainty, input uncertainty.

Changes to long-term trend growth can be due to exogenous shocks of growth. Name examples.

policy growth, new technologies, geopolitics, natural disasters, financial crisis, natural resources

Trend growth can anchor long-term capital appreciation. Formulate market value of equity using nominal GDP and earnings

GDP * earnings/GDP * P/E. Last two cannot grow forever, so long-run growth is limited to GDP growth

structural models vs reduced-form models in econometrics

Reduced-form models have less reliance on economic theory and are more compact.

Diffusion vs composite indices.

Diffusion is mainly about direction not magnitude.

Timeline for BEA GDP release?

Released with a quarter of delay. “Advance” estimate (released month after quarter end. This is what Atlanta Fed’s GDPNow forecasts), “preliminary” estimate, “final” estimate.

The three approaches for estimating business cycle are:

Econometric models (discipline and precise values but easily subject to misspecification), indicators (simple but data may be subject to large revisions), checklist (flexible but subjective)

Describe the five phases of business cyles.

1: initial recovery. This is at the trough of the cycle. Bond yields are low due to disinflation, and short-term yields are low.

2: early expansion. Output gap remains negative. Short rates start to move up in anticipation of stimulus-withdrawal.

3: late expansion. Output gap closes. Yield curve flattens as short rates continue to rise rapidly.

4: slowdown. Approaching peak and vulnerable to a shock. ]

5: contraction. Yield curve steepens as short-rates begin to drop.

Why is it difficult in practice to make money using business cycles?

1: cycles are difficult to predict. 2: hard to distinguish between cyclical vs secular forces 3: How markets react to cycles are complex.

Explain the asymmetry in central bank reaction function

CB tools are more effective at reigning demand than stimulating sluggishness, so they are more willing to let inflation run and respond more aggressively to demand weakness.

How do fiscal policies mitigate business cycles?

Besides deliberate actions, automatic stabilizers such as progressive tax or means-based transfers also help.

Explain zero-lower-bound in monetary rates

It claims that monetary policy rates cannot go below zero, as investors can just hold paper cash. But in practice, there is storage cost for storing cash in a vault, and the modern scale/speed of transactions cannot be supported by physical cash.

Why is default more likely in a deflationary environment?

Notional on debt remains constant, but revenue falls and assets lose value.

Discuss the implications for floating-rate instruments (“cash”), bonds, stocks, and real estate in the event of an inflation shock if a) the shock could be contained. b) the central bank will not be able to contain it.

a). short rates rise, and medium-term bonds suffer. Long-end yields would not move much. Stocks and real estate should not suffer if effects of inflation could be passed on. b) long-end yield rises. Stocks likely suffer. Real-estate impacts depend on lease terms.

What complicates the usage of negative interest rates?

Investors doubt whether they’re compensated enough on risky assets.

what is the impact of fiscal policies on real rates?

Loose raises real rates and vice versa.

national income accounting equation

X-M=S-I+T-G. Let Y be production and C private consumption. Then Y-T-C is private saving S, and Y-T-C-I is private saving net of investments. Add (T-G) is public savings. Added together is production not consumed domestically and thus must be shipped abroad.

Describe the four mechanism capital and current accounts are maintained in balance.

changes in income (GDP), relative prices, interest rates and asset prices, and exchange rates.

Under what conditions will two default-free countries have the same yield-curve

Unrestricted capital flow and fixed fx forever.

When horizon is less than duration, which risk dominates?

Market price risk dominates (risk is rising rates)

the four components of fixed income required returns are

default-free rate, term premium, liquidity premium, credit risk premium.

4 main drivers of term premium are

1: inflation uncertainty. 2: ability to hedge during recessions. Demand-driven economy yields low term premium. Supply-driven requires high term premium. 3: supply/demand 4:cyclical effects

Whats credit premium vs credit spread? What indicators predict corporate bond performance?

Credit premium is credit spread-expected loss. It’s the extra cushion on top. High OAS-adjusted spread helps predict corporate bond excess return over treasury, so does yield curve slope.

When is liquidity of bonds better? How to estimate pure liquidity premium?

1) priced near par 2) new 3) from a known issuer 4) simple in structure 5) high quality. Pure liquidity premium = yield spread between fixed-rate, option-free bonds from the highest-quality issuer and the next highest-quality large issuer of similar bonds (often a government agency or quasi-agency). The point is to strip out every other source of return and be left with only liquidity (quasi-agency bonds are less liquid)

Describe the changes to the four components of fixed income required returns in the following scenario: Although inflation rose modestly, the central bank cut its policy rate by 50 bps in response to weakening growth. Aggregate corporate profits have remained solid, and after a modest correction, the stock market finished higher for the year. However, defaults on leveraged loans were unexpectedly high this year, and confidence surveys weakened again recently. Equity option volatility spiked mid-year but ended the year somewhat lower. The interest rate futures curve has flattened but remains upward sloping. The 10-year government yield declined only a few basis points, while the yield on comparable government agency bonds remained unchanged and corporate spreads—both nominal and option adjusted—widened.

Short benchmark rates drop. 10-year yield stable despite lower short rate path suggests higher term premium. Higher credit spread but also higher probability of default suggests possible rise in credit premium. Lastly, wider spread between agency bonds and sovereign bond suggests higher liquidity premium.

List and explain the two issues more pertinent to emerging market issuers.

1) Ability to pay: fiscal deficit/GDP > 4%, debt/GDP > 70-80%, annual real growth rate < 4%, persistent current account deficit > 4%, foreign debt > 50% of GDP, reserve < 100% of short-term debt. 2) Willingness to pay: weak property laws, weak enforcement of contracts

Singer–Terhaar model

R Pi = φRP_i,G + (1 − φ) RP_i,S. RP_i,G = β_i,GM x RP_GM = ρ_i,GM x σi x (RP_GM/

σ_GM) and RP_i,S = σi x (RP_i,S/σi)

First equation assumes global markets are fully integrated. Second assumes complete segmentation of each market.

This model implies that greater integration with the global market reduces required yield

what factors affect cap rate?

Long-term benchmark yields, vacancy rates. Spread to treasury is positively correlated to corporate bond spread. Low-quality, high turnover properties are more likely to be cyclical and demand a higher discount rate.

Describe the required return components for real estate

Term premium high, illiquidity premium high, equity risk premium high, credit premium in accordance with comparable debt

When comparing direct real estate and REITs returns, what steps need to be taken?

Delever direct and REITs. Compare similar types. Research shows that investors do not seem to give up returns for REITs’ liquidity.

How correlated are REITs and direct real estate with stocks?

Direct real estate suffers from smoothing, which reduces correlation. In effect, both are highly correlated short-term, but less so long-term.

Real exchange rate

ratio of price levels converted to a common currency

Describe the effect of current account balance on fx.

Persistent, sized imbalances are more likely to affect fx. Deficit caused by profitable investments is less likely to affect fx. Spending pattern is slow to change and so is fx.

State and explain the long-run equilibrium condition

E(%ΔSd/f) = (rd − rf) + (Termd − Termf) + (Creditd − Creditf) + (Equityd − Equityf) +

(Liquidd − Liquidf). Dornbusch overshooting model suggests 3 phases when improved investment conditions occur. 1: fx appreciates as capital flows towards that country. 2: Investors question the elevated fx rate. 3: FX gives up partial or all of the gains, depending on the level of asset price adjustments. This phase is what the equilibrium condition tries to model. UIP is a reduced version of this model to only the rd-rf term.

What are hot money flows and how do central banks counter them?

Capital inflow due to higher interest rates. CBs counter them by intervening in the fx market and selling extra government bonds.

VCV matrix cautions

Number of observations should exceed number of assets (Σ=​(Y.TY)/(T−1), where Y is demeaned return matrix with rank at most T-1 (#observations). If T-1 le N, VCV guaranteed not be full rank, then w exists such that sigma*w=0, meaning portfolio risk is 0). A rule of thumb is 10 observations per asset to reduce sampling errors.

Formulate VCV Matrices from Multi-Factor Models and explain.

σ²ᵢ = Σₘ Σₙ βᵢₘ βᵢₙ ρₘₙ + v²ᵢ and σᵢⱼ = Σₘ Σₙ βᵢₘ βⱼₙ ρₘₙ . This makes use of the fact that cov(Σ... ,Σ... )=ΣΣ cov(…). ρₘₙ is defined as the cov between two factor returns. This addresses the zero-risk issue in sample VCV and reduces # calculations from (N(N-1)/2 to N*K + (K(K+1)/2). It imposes cross-sectional consistency.

is VCV from factor models biased and consistent?

Biased and inconsistent, whereas sample VCV is unbiased and consistent. So we are estimating sth that isn’t quite right with relative precision by using factor models.

Shrinkage Estimation of VCV Matrices

Combine the sample VCV with a target VCV with w*sample+(1-w)*target. This usually improves the efficiency (E[(θ̂ − θ)²] = Var(θ̂) + Bias(θ̂)²) of the sample VCV.

Time varying volatility

σ²ₜ = γ + α σ²ₜ₋₁ + β η²ₜ = γ + (α + β) σ²ₜ₋₁ + β (η²ₜ − σ²ₜ₋₁). Before day t starts, you dont have η²ₜ. You forecast with σ²ₜ = γ + (α + β) σ²ₜ₋₁, which assumes E[η²ₜ]= σ²ₜ₋₁. After day end, you update with the true volatility.

1. Compute daily surprises ηₜ (return minus mean).

2. Set σ²₀ to the sample variance and guess γ, α, β.

3. Run the recursion forward to get a variance for every day.

4. Score how likely the observed surprises are under those variances (log-likelihood).

5. Adjust γ, α, β to maximize the likelihood; the final run gives the volatility path.

Unconditional expected value of variance.

σ̄² = γ / (1 − α − β) . Volatility drifts and returns to this level if a+b<1 Solved by setting σ̄² = γ + α σ̄² + β σ̄²

The three levels of a governance structure are

investment committee, investment staff, and third-party resources

The six tasks of a governance model are

1: articulate long-short term objects. 2: allocate rights and responsiblities. 3: investment policy statement 4: strategic asset allocation 5: reporting framework 6: audit

Decision-reversal risk

risk of reversing a chosen course of action at exactly the wrong time

Define economic balance sheet and extended portfolio assets and liabilities

Economic balance sheet includes extended portfolio assets/liabilities such as human capital (the present value of future earnings), present value of future intellectual property royalties, etc.

How does asset allocation to bond/equity change as one ages?

Human capital is roughly 30% equity 70% bond. Then as human capital decreases as one ages, a 60/40 allocation, for instance, would require increasing bond allocation.

Three broad approaches to asset allocation

1) asset-only, (2) liability-relative, and (3) goals-based (investor maintaining lifestyle, not legal based)

Greet (1997) three superclasses of assets

Capital assets, Consumable/transformable assets, Store of value assets (neither income-generating or consumable but has value such as art)

The problems of overly granular asset classes are

Less distinctively defined sources of risk and less historical data.

The two common units of analysis for asset allocation are:

1: asset classes (hide overlapping exposures or concentration risks) 2: factor-based (not directly investable)

Steps to strategic asset allocation are:

1: quantify risk objectives 2: Quantify investor’s risk tolerance. 3: Determine investment horizon 4: Determine other constraints. 5: Determine the best approach to asset allocation 6: Specify asset classes and determine CMEs. 7: Develop a range of potential asset allocation choices. 8: Test these choices in simulation 9: Iterate back to step 7 until an allocation is agreed upon.

Why is it insufficient to consider sharpe ratio alone?

Sharpe ratio does not reveal overall portfolio risk such as VaR or volatility. It also fails to consider liquidity or diversification.

How may liability-driven allocation differ from asset-only?

Fixed-income takes a larger share, as the upside potential of equities does not benefit the sponsor unless the plan is underfunded. If liabilities accrue with inflation, equities might need a larger role as well.

Describe two classification systems for goals in goals-based allocation

Personal goals, Dynastic goals—to meet descendants’ needs, Philanthropic goals. Second system is Personal risk bucket, Market risk bucket, Aspirational risk bucket.

Illiquid investments are used to serve what horizon of needs?

Long term.

Distinguish strategic asset allocation, tactical asset allocation, and dynamic asset allocation

Tactical asset allocation involves short-term tilts away from the strategic asset mix that reflect short-term views. While strategic incorporates long-term equilibrium expectations, dynamic conditions on current market states.

Define active risk budgeting

how much benchmark-relative risk an investor is willing to take in seeking to outperform a benchmark.

how does tax affect the selection of active vs passive management?

Taxable investors have a higher hurdle for active management to create value, since it locks in more realized gains. Pensions/foundations/endowments/SWFs are not taxed.

The three questions percent-range rebalancing needs to consider are:

How frequently is the portfolio valued?

What size deviation triggers rebalancing?

Is the deviation from the target allocation fully or partially corrected?

what factors encourage and discourage rebalancing ranges?

higher transaction costs, illiquidity, taxes, beliefs in momentum encourage wider ranges. Risk-averseness, lower correlation of asset with rest of portfolio encourage tighter ranges. High volatility without transaction costs should decrease corridor, but in practice transaction costs should scale corridor up with volatility.

mean-variance optimization objective function

E(Rm)-0.005 x lambda x sigma_m² expressed in percentage not decimal. Lambda is typically 1-10.

If efficient frontier is risky asset only, how to pick the tangency portfolio?

One with highest sharpe.

Criticisms to plain MVO are:

1: highly sensitive to small changes in the inputs. 2: The asset allocations tend to be highly concentrated in a subset of the available asset classes. 3: Many investors are concerned about more than the mean and variance of returns. 4: sources of risk may not be diversified. 5:does not model liabilities. 6: single-period only and does not take into account trading costs, rebalancing, taxes.

Reverse optimization approach

Form a global portfolio from assets’ market capitalization, from which each asset’s beta is estimated. Expected return is calculated this way. However, one may have different views on expected returns compared to reverse optimization. In this case, black-litterman model is needed, as otherwise allocations from an optimizer still are changed too much.

Additional constraints used in practice to MVO often include:

1: set fixed allocations to certain assets, for instance to human capital/real estate to mimic an extended portfolio. 2: specify a range for an asset. 3: specify relative allocation between assets. 4: constrain to hold one or more assets representing liabilities.

Explain the Resampled Mean–Variance Optimization

Assume a multivariate return distribution. Simulate a whole history of returns first. Then recalculate the mean, cov matrices. This pair is fed to an optimization to generate one frontier. This process is then repeated multiple times, and resulting frontiers are averaged. This yields a very smoothed optimal allocation graph.

What can be inferred from the fact that both assets existed in large weights on a point of the efficient frontier?

They offer diversification and have low correlation.

How to include illiquid vehicles in optimization

1: don’t include them in optimization, but consider the funds as implementation possibilities of certain classes 2: model them in optimization using the funds’ profiles. 3: model them in optimization using the underlying class’ profile, focusing on diversification.

Define and formulate Marginal Contribution to Total Risk (MCTR) and Absolute Contribution to Total Risk (ACTR).

MCTR is the partial of portfolio volatility wrt to an asset weight. MCTR = corr x sigma_i or beta x sigma_p. ACTR = MCTR x weight. An allocation is optimal if excess return/MCTR is the same for all assets and equals the tangent portfolio’s sharpe.

What caution needs to be taken when using risk-factor based optimizations?

Collateral return to hold short positions should be added for total return.

Valuation exercise for a DB

1. Calculate the market value of assets.

2. Project liability cash flows (via actuarial principles and rules).

3. Determine an appropriate discount rate for liability cash flows

4. Compute the present value of liabilities, the surplus value, and the funding ratio.

Surplus optimization

U_LR = E(Rs,m) − 0.005λσ^2(Rs,m), where surplus return is (Change in asset value − Change in liability value)/(Initial asset value)

Explain the Hedging/Return-Seeking Portfolio Approach

When there is a surplus, a hedging portfolio is formed, and the surplus is invested to a return-seeking portfolio. This is known as the “basic” approach. If underfunded, we use a partial hedge (reduced capital to hedging portfolio) or a liability-glide path.

Explain how discount rates for liabilities are determined.

If there is an active market for the hedging portfolio, the pv of liability cash flows is simply the market value of the hedging portfolio. In many cases, however, the factors determining liability cash flows aren’t marketable (such as future salaries). In such cases, discount rates are set by regulators.

INTEGRATED ASSET–LIABILITY APPROACH

The portfolio of liabilities can be integrated alongside optimizing portfolio of assets.

how may advisors deal with the fact that clients don’t have probabilities in mind?

Use words “needs, wants, wishes, and dreams” and “nightmares, fears, worries, and

concerns”

how to select a module given required prob of success and time horizon? How to find required funding?

Select the module with the highest expected return (lowest funding cost) given these parameters. Then discount cash flows, accounting for inflation if needed, to present.

what are the two considerations for goals-based allocations after initial?

1: Time horizons often roll, especially in issues relating anticipated death of individual. 2: rebalancing is often needed considering conservative estimates of discount rates.

120-age rule

or similar 100-age, its the percentage that should be allocated to equity.

Explain risk-parity approach and criticisms

Older methods ignored volatility and modeled only returns. Risk-parity seems to make the opposite mistake.

minimum investments in hedge funds/PE are what amount?

tens of millions. Clients may otherwise need to consider fund of funds, or pooled vehicles.

How does rebalancing improve returns?

Diversification return and being short volatility.

How do taxes change correlations of assets? What about the efficient frontier?

Taxes do not change correlations. The efficient frontier may reduce allocation to HY bonds due to their high income tax (compared to lower dividend or capital gains rate) and lack of diversification to equity.

Formulate return, std, and rebalancing corridor given pre-tax treatments and tax amount.

r_at = pd x r_pt(1 − td) + pa x r_pt(1 − tcg). σ_at = σ_pt x (1 − t), where pd is proportion of r_pt attributed to dividend income and pa price appreciation.

Explain tax-deferred accounts

Trading within accounts does not trigger taxes. But withdrawals, also known as distributions, from these accounts trigger tax based on market value.

methods to evaluate TAA success include:

1: comparing sharpe ratios. 2: Evaluate the information ratio or the t-statistic of the excess return. 3: plotting the TAA alongside the realized efficient frontier

Representative bias

Individuals rely heavily on stereotypes, prototypes, or past experiences to make judgments

Define shortfall probability

Probability that a goal is failed

Define familiarity bias

A subset of availability bias. Home bias is one example.