Tracking Error

The tracking error of a portfolio is defined as the volatility of the active portfolio or the return of the portfolio relative to a benchmark. KRM processes portfolios that contain long and short positions, assets and liabilities in Asset Liability Management terminology. The forecasted values and returns are computed at the position level, consistently across scenarios for both the long and short positions and can be aggregated at the portfolio and sub-portfolio levels. Active portfolio risk profile and tracking error can be asses for a long and long\short portfolio relative to their benchmark. In addition, the entire distribution of simulated returns is available to compute other risk measures such as downside risk.

Performance Attribution

KRM stores valuations and simulation results at the individual position or transaction level. Aggregation hierarchies can be defined across portfolios, asset classes, country, currencies and any user-defined dimension of interest . KRM reports on valuations for the portfolio (long positions), the benchmark (short positions) and active (net) portfolio. The values are computed for each level of aggregation and meet the requirements of portfolio managers, analysts and risk managers.

Risk Decomposition

KRM is a very flexible platform that offers detail risk decomposition. Risk factors are represented by series of values or returns and combined in a covariance matrix with the necessary additional yield curve and probability of default models. These last two components are necessary to ensure proper and consistent cash flows valuations in multiple period simulations. It is a general framework that can accommodate a wide range of risk factors used to consistently value a broad range of asset classes.

Risk versus Return

KRM stores the simulations results at the position level, giving insight into the entire simulated return distributions, aggregated at user-defined grouping levels (portfolio, Instrument type, industry, country, …) as well as individual positions. It offers full flexibility to display all the relevant statistical risk measure (standard deviation, tracking error, downside risk measures). This provides more insight when standard risk metrics become less relevant to analyze unusual and extreme risk scenarios. Credit risk modelling and adjustments are also available through the explicit modeling of default probabilities in the multi-period simulation framework.

For instance, KRM provides the following risk\return analytics:

a) Downside Risk (VaR, CVar and Expected shortfall): Covered for any holding period, confidence level, and return weights (EWMA, GARCH, etc.) and any adjustment for prepayments, defaults or both.

b) Tracking Error: Volatility of the active portfolio. A KRM portfolio comprises the portfolio holdings (long position) and the benchmark holdings (short position). KRM generates and report the values and returns aggregated for both and the active portfolio. Forward looking multi-period, multi-factor driven tracking errors is readily available after a KRM multi-period forecast run has been processed.

Scenario Analysis

Scenario analysis is at the core of KRM’s design. The multiperiod framework with extensive aggregation capabilities allows for a detailed cashflow analysis at the position level that can be structured according to client requirements.

Historical factor covariances can be used to generate simulations along which the positions in the portfolio will be valued. The user can group risk factors. KRM will then provide risk contribution with respect to each factor group. This grouping can for instance be done across interest rate risk factors, macroeconomic factors, FX-rates, volatilities, spreads, credit risk parameters, stock prices, stock price indices.
In addition, KRM allows for the creation of factor-based scenarios, macroeconomic or others, that can be based on observed historical data or provided as future potential scenarios. As in the use of stochastic factor simulations, the valuation results can be aggregated accordingly.
The combination of portfolio rebalancing and factor simulations provides detailed simulated valuation outputs that can be used to measure a change in the investment strategy in different market conditions.

Equity and Fixed Income portfolios

All types of bonds including structured bonds can be modeled in KRM. Bond coupons that depend on indexes, spreads between long and short-term rates, path dependencies like moving averages, accumulated caps and floors, range accruals, snowballs, and many other exotic structures can be configured. Amortizing bonds, bonds that have a structured payoff schedule, sinking fund schedules, teaser periods etc. can be configured such that the system generates the exact future payoff schedules. KRM’s multi-period valuation engine works for all instruments including bonds that have embedded options, are denominated in foreign currency, or where the size of the coupon is linked to an inflation index or the performance of an equity investment.

KRM can accommodate Equity multiple factor models that combine indexes such as sector, style, country, currencies, and any other relevant factors such as ESG. These factors are also used alongside other factors relevant to other asset classes to generate simulation used to value multi-asset class portfolios.

As with other asset classes, portfolio attributes can be used to aggregate risk and valuation measures at different levels.Portfolios allocation targets can be set up for each future period in the simulations.