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Attribution

What types of attribution can FIA perform?

FIA calculates all types of attribution currently used by the marketplace – Brinson, duration/non parallel yield curve shifts, shift/twist/curvature curve movements, key rate durations, credit shifts, coupon and yield effects, pull-to-par, roll-down, inflation, exchange rate returns, and others. Please see our page on risk types for more information.

Can FIA run Brinson-Fachler attribution on portfolios of equities?

Yes. To do this,

  • ensure a benchmark has been supplied;
  • in the configuration file, set  to the required classification name(s), and set the  term to ;

    • BrinsonAllocationSectors

    Residual

    Stock selection

More details are provided on the asset allocation page.

What instrument classes do you cover?

Again, the list is long and complex. It is our intention to cover the vast majority of securities in use in the marketplace. If you have a security type that cannot be handled by FIA, please let us know and we will consider whether to include it in the next release.

Is FIA multi-currency?

Yes. The user supplies security returns in both local and base currency terms, and FIA uses this information to calculate returns due to changes in exchange rates.

FIA currently uses a naive currency attribution model. Future releases may include more sophisticated FX attribution algorithms, such as Karnosky-Singer.

Is it necessary to specify the base currency for a multi-currency attribution calculation?

No. Base and local currency returns are supplied in the portfolio and benchmark returns files. It is assumed that base currency returns have already been calculated with respect to an underlying base currency, so there is no need for the user to supply this information.

For reporting purposes, future releases may supply the ability to specify the base currency in the configuration file. In this case, the local and base currency returns for securities that are priced in the base currency should be identical, and a check will be made that this is so.

What is the difference between first-principles attribution and perturbational attribution?

FIA offers two ways to run attribution on a security.

The first is called first-principles attribution. In this model, all pricing is run off the yield curve using FIA’s sophisticated internal pricing, so there is no need to supply any risk numbers. This is a data-light approach and requires far less data than any other model.

The second is called perturbational attribution. Here, no pricing functions are used. Instead, the user supplies risk numbers (yield, duration) which act as a proxy for a pricing model. This approach is widely used in the marketplace but potentially requires very large amounts of data

Can FIA mix-and-match first-principles and perturbational attribution?

Yes. The two attribution models can be used at the same time in the same portfolio over different securities. In fact, the same security can be treated using different models at different times; just use the effective date function to change its type from, eg, BOND to PERTURBATIONAL BOND or vice versa.

Curvature return vs convexity return - what’s the difference?

These two terms are often confused by newcomers to the field.

Curvature return is return generated by non-parallel movements in the yield curve. Convexity return is any additional return generated by the non-linearity of the relation between yield and change.

What is sector return?

Sector return is return generated by sector curves.

A sector curve is a yield curve that applies to securities in a particular industry sector. For example, US AA-rated banking bonds define a sector curve.

Sector return is the return generated by movements in this curve, in addition to the other drivers of return in a portfolio. This is not the same as asset allocation return, which measures return due to over or underweighting particular sectors.

What is carry return, and how can it be decomposed?

Carry return is return due the passage of time. In other words, it is the return you see if nothing changed in the market, and all yield curves stayed fixed.

Carry return can typically be decomposed into coupon return (return generated by known security payments) and capital gains or losses on securities.

Carry return can also be decomposed into risk-free return and credit return. For instance, a corporate bond that is structurally identical to a treasury bond will trade at a higher yield than the treasury bond, to compensate the investor for the extra risk involved in investing in non-sovereign debt. The carry return generated by the treasury bond is the risk-free carry return, and the return generated by the spread to the risk-free return is the credit carry return.

How do I calculate return due to prepayments?

Prepayments generate two types of return.

The first is due to paydown. If an MBS is trading at a discount, then it will generate a capital gain between now and maturity, as its price has to rise to par. If a prepayment is received, you are receving part of the security’s principal back at par, not at the current discounted rate, and this gives extra return.

The second is due to changes in the distribution of cash flows. If prepayments are allowed, the future pattern of cash flows is adjusted each time a cash flow is recieved, and this will change the price of the security. Whether the adjustment is up or down depends on the pattern of cashflows, previous prepayments, the time to maturity of the security, and the level of the current yield curve.

Is rolldown a carry or a market effect?

Rolldown can be seen as either.

Rolldown return occurs even if there are no changes in the shape of the yield curve. It should therefore be classified as carry return. However, it is also generated by the shape of the yield curve. A perfectly flat curve will generate no rolldown return. Therefore, it should be classified as market return.

In practice, it is probably best to measure rolldown as an entirely separate effect and to allow the user to decide where to put it.

How do I calculate convexity return?

Convexity return is calculated automatically by FIA. However, here is how the calculation works.

Return due to market effects (changes in yield) is calculated from rmarket = −MD × δy + 2 × C × δy2

Convexity return is generated by the second term, and requires the level of the security’s convexity C and its change in yield δy. In practice, it may be easier to reprice the security at the start and end of the current interval, assuming (i) the yield curve is flat, so any return made is due to a parallel shift; (ii) the yield curve is unchanged, so return is due to all market effects. The first return is the overall market return, and the second is due to parallel shift, which is the same as the first term in the above equation. The convexity return is then given by the difference between the two returns.

This route does not require the calculation of any risk numbers.

What attribution effects does an MBS generate?

MBS and ABS are complicated by their ability to accept prepayments, their often complex cash flow patterns, and their embedded call option(s). In addition to the usual returns (carry, market, credit) they also generate return due to paydown, changes in repayment rate, and market volatility.

In addition, a simple duration measure of interest rate senstivity is often inadequate to express their price dependence on the yield curve, and a more complex key rate duration analysis may be reqiured.

Where do trading returns belong in an attribution environment?

Trading returns are generated entirely by the portfolio manager, and cannot be measured by an attribution system. Although they are a real source of return, they should measured externally and do not belong in an attribution report.

What types of yield curve decomposition are available, and what do they mean?

FIA offer the following options:

  • None. Any return due to changes in the sovereign curve is assigned to residual. This approach is appropriate for portfolios that are purely credit driven and have no exposure to changes in the sovereign curve.
  • Aggregated. Using the yield curve at the start and end of each calculation interval, each security is repriced using both curves and the return is generated. No sub-effects are calculated and a single return figure is generated. This type of decomposition is suitable for the simplest possible attribution.
  • Duration attribution. Calculates return due to (i) parallel shifts in yield curve, (ii) non-parallel shifts
  • Shift, twist, curvature attribution. Calculates return due to (i) parallel shifts in yield curve, (ii) steepening and flattening of yield curve; (iii) other types of movement in yield curve
  • Key rate duration attribution. A key rate duration analysis isolates the effects of changes at particular maturities along the yield curve, rather than measuring the effect of different types of movements. Key rate duration analysis may be appropriate when running attribution on portfolios of securities that have cash flows spread across a range of maturities, rather than having the bulk of their yield curve exposure concentrated at maturity. Securities in the former category include mortgage-backed bonds and other amortizing securities, and related securitized securities.
  • CCB attribution. CCB attribution uses the Colin-Cubilie-Bardoux algorithm to calculate the twist and curvature movements of a yield curve. This algorithm uses a conventional approach to calculating the parallel shift of a yield curve, but performs a least-squares fit of a first order polynomial to calculate the twist of the curve. This removes many of the inherent problems involved when fixed twist points are defined.
  • PCA attribution. Principal component analysis (PCA) uses a suitably large number of historical yield curve changes to determine a small set of basis functions that can be linearly combined to represent these curve movements in the most economical way.

PCA on historical yield curve data shows that curve movements fall into a number of fairly clearly defined types. Typically, the first basis function is close to a flat line, the second rises monotonically (but is seldom a straight line), and the third imposes some curvature motion. These functions are usually interpreted as shift, twist, and curvature.

However, these movements are typically slightly different from more conventional interpretations of these terms. The shift movement from a PCA is usually close, but not identical to, a parallel curve shift, and the twist movement is not uniform across all maturities. For these reasons, a PCA analysis may not directly represent investment outcomes in terms of the decisions that were taken by the trader.

FIA also offers capital attribution, in which all return from yield movements is calculated from changes in the supplied yield to maturity. In this case no detailed curve or credit returns are available, but no yield curve data need be supplied.

Can FIA calculate Karnosky-Singer currency attribution?

This functionality is planned for the next major release.