Portfolio Management Pathway

which has lower expense ratios for long-term investors, ETFs or mutual funds?

ETFs

Define overlays and main types.

An overlay is a derivatives position layered on top of an existing portfolio to adjust its risk or return characteristics, without disturbing the underlying holdings.

A completion overlay addresses an indexed portfolio that has diverged from its proper exposure. Typically used to address cash drag.

A rebalancing overlay addresses a portfolio’s need to sell certain constituent securities and buy others.

A currency overlay assists a portfolio manager in hedging the returns of securities that are held in a foreign currency

What are the pros/cons of using derivatives for portfolio management compared to using the cash markets?

With tactical allocation changes, derivatives can change exposure to an index with a single transaction. However, for long-term investors, derivatives require rolling. Derivatives also may not exist on certain securities.

advantage of swaps compared to futures

Swaps are traded otc and thus offer customization on the underlying index, maturity, etc. There is of course more counterparty risk.

Describe how separately-managed equity indices work

Managers first subscribe to a data service from the index provider. The data feeds an order management system (OMS) that automatically creates trading files and transmits them to a broker using the FIX protocol (Financial Information eXchange), who buys the securities using program trade. Program trade is the simultaneous buying/selling of many stocks. These managers also maintain good relationships with the brokers to minimize transaction costs.

Describe full replication method.

Hold all securities in the index. As the manager moves towards more illiquid securities, tracking error gross of transaction costs still decreases but net tracking error can start to go up at one point. In full replication, managers order Market On Close orders to fully match index performance measures.

Stratefied sampling.

Find strata will be mutually exclusive and also exhaustive. Now weight portfolio holdings proportionately to each stratum's weight in the index.

Optimization approach

Minimum portfolio tracking error subject to constraints such as maximum number of names, market capitalization, portfolio volatility.

pros/cons of optimization approach vs stratefied sampling.

Optimization approach has lower tracking error and takes into account asset correlations, but covariance data is computed on historical data, which might change over time.

Excess return vs tracking error

Excess return is Rp-Rb and can be negative or positive. Tracking error is never negative.

sources of tracking error.

management fees, sampling, intraday trading, commissions, cash drag,

During low interest rates, which sector outperforms, financials or utilities?

Utilities/telecom are high dividend payers. They outperform during periods of low rates, compared with financials, who struggle to lend profitably.

rewarded factors vs unrewarded

Some factors (most commonly, size, value, momentum, and quality) have been shown to be positively associated with a long-term return premium and are often referred to as rewarded factors.

What are the issues with the hedged portfolio approach in forming factor portfolios?

It only takes into account the top and bottom quantiles, although performance does not need to be linear across.

Explain factor tilt portfolios and factor mimicking portfolios.

The factor-tilting portfolio tracks a benchmark index closely but also provides exposures to the chosen factor.

The factor mimicking portfolio is the theoretical construct of having positions in every stock and a resulting exposure to only the one factor you’re interested in.

Tactics used by activist strategies include

Seeking board representation and nominations, engaging in proxy contests, proposing restructuring of balance sheet, reducing management compensation, initiate legal proceedings against existing management for breach of fiduciary duty, breaking up a conglomerate, launching media campaign,

How do markets react to activist announcements?

There is appreciation prior to the announcement, an average 2% on the announcement date, and further appreciation post-announcement.

Describe pairs trading in statistical arbs

Start from a moving average (for instance 130 day) of spreads (log of price differentials of a pair). Then establish a band of +2/-2 standard deviations. Whenever spread exceeds this band, take position. Exit when the spread moves back to the moving average.

Building blocks of portfolio construction

Rewarded factor weightings, alpha skills (timing to rewarded/unrewarded factors), position sizing (how exposed is the manager to idiosyncratic risks), breadth of expertise (#independent bets in fundamental law of active management)

Refresh on the fundamental law of active management.

E (RA) = IC x √BR x σ_RA x TC

Characteristics of top-down vs bottom-up and systematic vs discretionary

Formulate a security’s contribution to portfolio variance or active return variance.

Vp = ∑∑xi xj Cij. This follows directly from variance of a sum decomposition.

For security i only, CV_i=xi∑xj Cij=xi ∑xj cov(Ri, Rj)=xi cov(Ri, ∑xj Rj)=xi Cip = CTR * sigma_p.

For the variance of active return, replace weights with active weights.

The three practical limits of risk are

Implementation constraints, limited diversification benefits, reduction of compounded returns from leverage.

Regarding last point, Rg ≈ Ra − σ² / 2. This refers to “volatility drag”. Note that variance scales squared to leverage, whereas return is only linear.

Recall CV_i=xi∑xj Cij. In the factor context, weights are loadings.

0.733 x (0.733 × 0.00178 + 0.00042 x -0.328 + 0.00066 × 0.045 + -0.00062×0.042) = 0.000858, so 91%.

Define formal vs heuristic risk measures.

Formal constraints are statistical in nature and are often tied to return distributions of the portfolio. Heuristics show up as controls imposed on permissible portfolio composition (sizing of positions, max sector deviations, max leverage, etc).

What is long extension?

Short proceeds are used to buy long. Net exposure is 100%.

Merits of long-only investing.

long-term risk premium, capacity/scability (shares not always available to short at large quantities), limited liability, transactional complexity, management costs, personal idealogy (short selling is wrong)

net exposure vs gross exposure

The absolute value of the longs minus the absolute value of the shorts is called the portfolio’s net exposure. The sum of the longs plus the absolute value of the shorts is called the portfolio’s gross exposure.

Pros/cons of a long/short strategy

Pros include ability to more fully express short ideas, efficient use of leverage and of the benefits of diversification, greater ability to calibrate/control exposure to factors.

Cons include more complexity associated with usage of short positions, possibility of reduced market return

How does ls achieve higher information ratios?

The ability to short improves transfer coefficient. Moreover, in a long-only, market risk dominates. The ability to neutralize the dominant factor allows a more spread out, even risk distribution

If 60% of deviations from the mean are negative, what skew is this?

Positive skew

How does yield curve shape affect the difference between portfolio IRR and weighted average YTM of a bond portfolio? What about portfolio duration vs weighted average duration? Portfolio convexity vs weighted average convexity?

When yield curve is upward sloping, portfolio has higher IRR, convexity, and duration than the weighted average versions.

How to annualize dispersion and convexity? How to compute modified duration from duration?

By dividing the SQUARE of the periodicity (4 for semiannual)

ModDur = -dur/(1+r/m)

What is required for perfect immunization?

Ideally, it’s a zero-coupon bond, and macaulay duration of the portfolio should perfectly match the zero bond. However, as time passes, the duration falls out of place with the zero bond’s duration, which decreases linearly regardless of interest rate risk. Rebalancing is thus required to adjust the duration. Furthermore, changes in cash flow yield of the portfolio must match changes in the zero bond’s YTM.

What is structural risk? How to minimize it?

The risk is that yield curve twists and non-parallel shifts lead to changes in the cash flow yield that do not match the yield to maturity of the zero-coupon bond that provides for perfect immunization. Reducing dispersion around Macaulay duration reduces structural risk (ideal case is a zero-coupon bond, of course), which is identical to minimizing convexity holding duration and yield constant.

Characteristics of a bond portfolio structured to immunize a single liability are

• Has an initial market value that equals or exceeds the present value of the

liability.

• has a portfolio Macaulay duration that matches the liability’s due date.

• minimizes the portfolio convexity statistic.

What is the difference with multiple liabilities portfolio?

Money duration matches as close as possible whereas in single exceeds.

Convexity and dispersion exceed that of liabilities.

Why would a manager uses derivatives to match duration? How many contracts are needed?

A manager might prefer short-term bonds due to liquidity or regulatory constraints.
Asset portfolio BPV + (Nf × Futures BPV) = Liability portfolio BPV, where in case of bond futures, Futures BPV = BPV_ctd/CF_ctd. Knowing the ctd is crucial to compute the right futures bpv.

What is contingent immunization?

The presence of a significant surplus, the difference between the market values of the assets and liabilities, allows the asset manager to consider a hybrid passive–active strategy known as contingent immunization.

Accumulated Benefit Obligation (ABO) vs Projected Benefit Obligation (PBO)

ABO is the pv as specified by current wage and number of years worked. Projected is the pv as specified by the projected final wage. One may calculate effective durations on these measures.

How to compute notional on a swap to reduce duration gap?

Asset BPV + [NP × Swap BPV/100 ] = Liability BPV. Note that duration of a swap is computed from durations of the fixed leg and floating leg.

Asset BPV = 528,384; Liability BPV = 1,215,000; Swap BPV = 0.1751 per 100 notional. Find the receive-fixed swap notional for a 75% hedge of the duration gap.

(1,215,000-528,384)/0.00175=392,127,927. For 75%, 294m.

How to use swaptions instead of swaps to reduce duration gap.

A receiver swaption is ITM when market rates are below the strike. The premium is defined on per dollar of notional. A swaption collar is buying a receiver swaption and then writing a payer swaption.

Explain how a manager chooses between swap, swaption, or swaption collar.

If the manager believes rate stays below swap fixed rate, then swap is the most attractive.

At a certain point above the written payer swaption strike, the swaption becomes more attractive compared to swaption collar, as it is limited loss.

Risks in liability-driven investing

Durations for equity/alternatives may not be zero.
Assumption uncertainties in type 4 liabilities.
Corporate/Treasury yield spread when using bond futures.
Corporate/mrr spread when using swaps.
Counterparty risk in OTC derivatives without credit support annex(csa) and collateral risks.

Primary indexing risk factors for a bond portfolio are

Duration, key rate duration, percentage of sectors, credit quality makeup, Sector/coupon/maturity call weights, issuer exposure.

Explain the present value of distribution of cash flows methodology

Lay out the index's cash flows across time buckets ("vertices" — e.g., 0.5yr, 1yr, 2yr…) broken by call status.

Take the present value of the cash flows at each vertex, then express each as a percentage of the portfolio's total PV.

Weight each vertex by its contribution to duration (roughly, PV share × time), so vertices further out count more. This turns the PV distribution into a risk distribution across the curve.

Match your portfolio's distribution to the index's, vertex by vertex. If the index has 15% of its rate risk at the 5-year point, your portfolio should too.