Rule-based management of cash flows in Income Plus Funds€¦ · 06 A withdrawal example. 01...

PRESENTED BY:

Rule-based management of cash flows in Income Plus Funds

Keith Forbes

Fixed Income Quantitative Analyst

4 June 2020

Disclaimer

Fairtree Asset Management (Pty) Ltd is registered as a financial services provider with the Financial Services

Board of South Africa, with registration number 2004/033269/07 and FSP number 25917.

A schedule of fees, charges and maximum commissions, as well as a detailed description on how performance fees are

calculated and applied, is available on request from the manager of each fund (“the Manager”), being either Sanne

Management Company (RF) (Pty) Ltd, Realfin Collective Investment Schemes (RF) (Pty) Ltd, Prescient Management

Company (RF) (Pty) Ltd or Boutique Collective Investments (RF) (Pty) Ltd, all being registered and approved managers of

Collective Investment Schemes. The name of the fund shall reflect the name of the approved manager of the fund.

Additional information, including key investor information documents, minimum disclosure documents as well as other

information relating to the portfolio is available, free of charge, on request from the Manager

The Manager retains full legal responsibility for any co-named portfolio and is responsible for the appointment of a trustee

in accordance with the provisions of the Collective Investment Schemes Control Act, 45 of 2002.

We believe the information displayed is accurate and reliable, but no warranty of accuracy or reliability is given and no

responsibility arising in any way for errors and omissions (including by way of negligence) is accepted by Fairtree Asset

Management (Pty) Ltd.

This information is not intended to provide advice to, or take into account individual investors’ objectives or

circumstances. This material should not be construed to represent a solicitation to invest in the portfolio and is disclosed

for reporting purposes only.

Collective Investment Schemes are generally medium to long-term investments. Please note that past performance is no

guarantee of future performance and that the value of participatory interests may go down as well as up. Collective

investments are traded at ruling prices and can engage in scrip lending and borrowing.

A Collective Investment Scheme may be closed to new investors in order for it to be managed more efficiently in

accordance with its mandate. The Manager does not provide any guarantee with respect to the capital or the return of the

portfolio. Excessive withdrawals from the portfolio may place the portfolio under liquidity pressure and in such

circumstances, a process of ring-fencing of withdrawal instructions and managed pay-outs over time may be followed.

Commission and incentives may be paid, and if so, are included in the overall costs. Investors should note that the value

of an investment is dependent on numerous factors which may include, but not limited to, share price fluctuations, interest

and exchange rates and other economic factors. Performance is further affected by uncertainties such as changes in

government policy, taxation and other legal or regulatory developments.

The performance of the portfolio is dependent on the making of correct assessments of the price movements of individual

securities and other investments. Financial markets have historically exhibited high levels of volatility and negative

movements that have affected the price of all assets within a specific class. The portfolio’s investments will thus be

subject to market risk. Through financial gearing via the long/short process, the portfolio may be leveraged. This will

mean enhanced positive gains but conversely can mean magnified losses. No taxation has been deducted in the

computation of returns. The taxation treatment of returns is the investor’s responsibility.

All returns are disclosed net of performance fees.

The Fairtree Global Flexible Income Plus fund is a sub-fund of Prescient Global Funds PLC and is managed by Prescient

Fund Services (Ireland) Limited. Prescient Fund Services (Ireland) Limited is authorised in Ireland and regulated by the

Central Bank of Ireland. The Fairtree Global Flexible Income Plus fund is approved as a foreign collective investment

scheme under Section 65 of the Collective Investment Schemes Control Act 45 of 2002 by the Financial Sector

Conduct Authority of South Africa. Fairtree Asset Management (Pty) Ltd (FSP: 25917) is the investment manager of the

Fairtree Global Flexible Income Plus fund.

Overview

01 Motivation

02 Risk, return and correlation

03 Portfolio strength

04 Mathematical optimisation

05 Our implementation

06 A withdrawal example

MOTIVATION01

Our situation

▪ We manage 14 credit funds with different risk / return targets

▪ Fund flows alone will cause the funds to differ

▪ The funds are also governed by different legislation that imposes different constraints on

portfolio composition

▪ Positions tend to be illiquid bonds that are usually acquired at issuance and held to

maturity

Our situation

▪ Our funds are all different from one another, and the assets are such that they cannot

necessarily be bought / sold in the marketplace

▪ A well-diversified portfolio must be built up over time

▪ One cannot simply acquire all desired assets at a single point in time

Software is used to compute optimal trade sizes in three manners

Rule-based appetite, allocation and withdrawal

WITHDRAWAL

Remove the assets that are

seen as the least useful for the

fund and determine whether

they can benefit other funds

under management

(re-allocation)

APPETITE

Determines how much of an

asset to bid for based on the

funds’ appetite for the

security

ALLOCATION

Once an issuance is

acquired, allocate it across

the funds in a way that

provides maximum benefit to

all funds

Sizing positions

▪ Our approach is designed to treat customers fairly by algorithmically sizing portfolio positions

▪ This avoids manager bias, where one fund may inadvertently be favoured over another or the

manager’s risk preference becomes confused with the client’s

▪ It allows us to optimally move each fund towards its unique target keeping, ex ante Sharpe

ratios as high as possible and fulfilling all regulatory constraints

Sizing matters

▪ Simply thinking buy / sell / hold is not enough

▪ There is an optimal size for each position – too large or too small a position will lead to risk

and return characteristics that are not as good as they could be

▪ We need to be able to measure the effects of sizing. That is, we must compute the portfolio

distribution

▪ The portfolio distribution is the ex ante probabilistic distribution of return outcomes

Why compute portfolio distributions?

▪ An investor is ultimately concerned with portfolio performance, not the performance of

individual positions per se

▪ Heuristics and rules-of-thumb are sub-optimal

▪ Instruments interact in complex non-obvious manners. Intuition is our enemy – the maths

must be done

▪ Knowing the portfolio distributions allows us to optimise the risk targeting and

diversification within each fund in a common framework

Risk targeting example

Proportion of target risk achieved

Qualit

y o

f risk (

Div

ers

ity)

Goal: (1,1)

100%

Perfect diversification:

all unpriced risk removed

too much risktoo little risk

Fund C

Fund BFund A

100%

Risk targeting example - an instrument matures


Qualit

y o

f risk (

Div

ers

ity)

Goal: (1,1)

100%




Fund C

Fund BFund A

100%

Risk targeting example – new issuance allocated


Qualit

y o

f risk (

Div

ers

ity)

Goal: (1,1)

100%




Fund C

Fund BFund A

100%

RISK, RETURN &

CORRELATION02

Moments of portfolio return distributions

Mean of the return distribution:

Variance of the return distribution:

An even-handed model for risk and return

▪ Driven by current market levels rather than backward-looking

▪ No position is considered to be inherently more favourable than any other

▪ More specifically, we use a CAPM-like approach in which the undiversifiable risk in every

position is priced equivalently

▪ Risk and return come directly from the distributions implied by the spread

Multi-sector hierarchical model (illustrative)

▪ More closely related obligors, have higher pairwise correlation

▪ Model proposed by Gregory & Laurent (2004)


Mean of the return distribution:

Variance of the return distribution:

Returns, risk, correlation – model summary

▪ Positions have expected returns – this is estimated from the par spread (the expected return

is the mean of the return distribution)

▪ Positions have risk – this is also estimated from the par spread (the risk is the standard

deviation of the return distribution)

▪ Position P & L is correlated with other positions – this is imposed by the hierarchical

correlation model

BCI Income Plus positions on 08 May 2020

NPV

Par

Spre

ad

BCI Income Plus on 08 May 2020 – Vanilla Bonds

Ex ante Sharpe

Expecte

d R

etu

rn

BCI Income Plus on 08 May 2020 – Vanilla Bonds & Sector Sub-Portfolios

Ex ante Sharpe

Expecte

d R

etu

rn

BCI Income Plus on 08 May 2020 – Vanilla Bonds & ABS’s

Ex ante Sharpe

Expecte

d R

etu

rn

BCI Income Plus on 08 May 2020

Ex ante Sharpe

Expecte

d R

etu

rn

PORTFOLIO

STRENGTH03

Twin goals

▪ An investment manager aims on having -

1. Ex-ante Sharpe ratios as high as possible, and

2. Actual risk as close as possible to target risk

The dilemma

28

Which is better ?

1. Obtaining a high Sharpe with tiny

risk

2. Or a mediocre Sharpe with on-

target risk?

Of course the answer depends on the

actual numbers

In order to answer these questions and to

allocate positions to a fund or to a suite

of funds, it is necessary to specify a single

number that somehow combines

distance from the risk target with the

distance from best-case Sharpe ratio


Portfolio strength:

Research

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3407419

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3407419

Sensitivity to position size

Position

Port

folio

Str

ength

Sensitiv

ity to P

ositio

n S

ize

MATHEMATICAL

OPTIMISATION04

2-Dimensional optimisation problem (illustrative)

Maximisation in n dimensions

▪ BCI Income Plus has 167 positions – this means our withdrawal problem involves finding the

maximum of a 167-dimensional surface

▪ Although we cannot visualise high-dimensional functions, we know that if they are smooth,

then they are locally approximately quadratic (think of a parabola / paraboloid)

▪ If we know our surface’s gradient (first derivatives) and curvature (second derivatives) then

we know the quadratic’s formula and can step directly to its maximum

Maximisation in n dimensions

▪ This maximum will in general be a good approximation to our surface’s maximum, but we

can obtain an even better approximation by repeating the procedure iteratively until

improvements are negligible

▪ The modern optimisation algorithms that we use are extensions of this idea

1-Dimensional optimisation problem (illustrative)

Position Size

Port

folio

Str

ength

OUR

IMPLEMENTATION05

COPS Software – Our implementation

▪ COPS stands for Constrained Optimisation of Position Sizes

▪ COPS determines the optimal position sizes for new allocations and withdrawals across our

suite of credit funds

▪ We have derived analytical solutions for the objective function (portfolio strength) and its

gradients including modelling special cases such as CLNs and ABSs

▪ Legal constraints are specified mathematically

COPS Software – Our implementation

▪ Function and gradients that are used as input to a non-linear constrained optimisation library

(namely MIT’s NLOPT library)

▪ Monte-Carlo sampling methods are not used. We use closed-form analytical solutions to

ensure speed and smoothness of the objective function

▪ The mathematics is coded in C++ with a Mathlab frontend. An object-orientated approach is

followed

Portfolio mathematics

Portfolio strength gradient (chain rule):

Sharpe from hazard rate and spread:

Accounting for ABS effects: Smoothed UCITS constraint:

ABS effects on gradients:UCITS gradient:

Implementation - ~ 25, 000 lines of C++ and Mathlab

EXAMPLE06

Withdrawal example

Position #

Am

ount

Withdrawal example

Reallocation of non-cash assets to other funds

portfolio strength

before after improvement

Fund 1 0.7508 0.9313 0.1805

Fund 2 1.3162 1.3706 0.0545

Fund 3 1.2883 1.3256 0.0374

Fund 4 1.2828 1.3063 0.0235

Fund 5 1.2355 1.2355 0.0000

Fund 6 1.0892 1.1582 0.0689

Fund 7 1.1817 1.2015 0.0198

ABKS1 AGL03 FRB24 FRC319 IV035 IV046 NGLT1B SBT103 SBT206

Fund 1 6,000,000 0 0 0 0 4,000,000 17,000,000 2,000,000 0

Fund 2 0 0 2,000,000 0 2,000,000 5,281,546 1,000,000 8,000,000 0

Fund 3 0 0 0 5,000,000 0 0 0 0 0

Fund 4 0 0 0 10,000,000 0 0 0 0 0

Fund 5 0 0 0 0 0 0 0 0 0

Fund 6 0 6,000,000 0 0 0 3,000,000 2,000,000 1,000,000 0

Fund 7 0 5,000,000 0 0 0 1,000,000 1,000,000 0 0

Summary

60

We use our in-house COPS

software to optimally size

instruments across all funds

during withdrawals and

allocations

THE CONCEPT OF PORTFOLIO STRENGTH ALLOWS

US TO MEASURE THE STATE OF OUR PORTFOLIOS

WITH RESPECT TO BOTH DIVERSIFICATION AND

RETURN TARGETING

Algorithmic allocation and withdrawal ensures that customers are treated fairly and that portfolios are

optimally positioned with respect to diversification and return targeting

The portfolios strength of our suite of funds has improved from withdrawals. This is because

withdrawals allow us to optimally dispose of and re-allocate assets

Thank You

Rule-based management of cash flows in Income Plus Funds€¦ · 06 A withdrawal example. 01...

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