Yield curve forecast combinations based on bond portfolio performance

• Author: João F. Caldeira,André A. P. Santos,Guilherme V. Moura
• Date: 01 January 2018
• DOI: http://doi.org/10.1002/for.2476
• Published date: 01 January 2018

Received: 30 November 2015 Revised: 13 January 2017 Accepted: 25 March 2017

DOI: 10.1002/for.2476

RESEARCH ARTICLE

Yield curve forecast combinations based on bond portfolio

performance

João F. Caldeira1Guilherme V. Moura2André A. P. Santos2

1Department of Economics, Universidade

Federal do Rio Grande do Sul, Porto Alegre,

RS, Brazil

2Department of Economics, Universidade

Federal de Santa Catarina, Florianópolis,

SC, Brazil

Correspondence

Guilherme V. Moura, Department of

Economics, Universidade Federal de Santa

Catarina, Florianópolis, SC 88049-970,

Brazil.

Email: guilherme.moura@ufsc.br

Abstract

We propose an economically motivated forecast combination strategy in which

model weights are related to portfolio returns obtained by a given forecastmodel. An

empirical application based on an optimal mean–variance bond portfolio problem

is used to highlight the advantages of the proposed approach with respect to com-

bination methods based on statistical measures of forecast accuracy. We compute

averagenet excess returns, standard deviation, and the Sharpe ratio of bond portfolios

obtained with nine alternative yield curve specifications, as well as with 12 dif-

ferent forecast combination strategies. Return-based forecast combination schemes

clearly outperformed approaches based on statistical measures of forecast accuracy

in terms of economic criteria. Moreover, return-based approaches that dynamically

select only the model with highest weight each period and discard all other models

delivered evenbetter results, evidencing not only the advantages of trimming forecast

combinations but also the ability of the proposed approach to detect best-performing

models. To analyze the robustness of our results, differentlevels of risk aversion and

a different dataset are considered.

KEYWORDS

bond returns, forecast combinations, portfolio optimization, yield curve

1INTRODUCTION

Forecast combination strategies have been used in economics

and finance to account for model uncertainty and to alleviate

the effects of structural breaks and model misspecification.

However, combination weights are traditionally determined

by statistical measures of forecast accuracy, disregarding the

decision-making process in which forecasts are to be used and

their economic value. This paper proposes an economically

motivated forecast combination strategy in which weightsare

related to the portfolio returns obtained by using a given

forecast model. Specifically, we consider a bond portfolio

allocation problem in which the investor is uncertain about

which model is best suited to forecast the yield curve in a

given period of time.

One common aspect in the majority of the existing literature

on forecast evaluation is the fact that economic performance

of different forecasting models is usually evaluated using the

same model during the entire evaluation sample. In the case of

bond portfolio selection, as well as in the case of other finan-

cial securities, there are many different models available, and

it is often unclear which one should be used to forecast asset

returns. Additionally, misspecification and structural breaks

might change our view regarding which models perform best

at each point in time. Therefore, employing an economically

motivated dynamic model combination offers a well-suited

alternative to overcome these difficulties.

Our choice to consider the bond portfolio allocation as an

economic problem to support a forecast combination is moti-

vated by the fact that not onlybond por tfoliooptimization, but

also the pricing of financial assets and their derivatives and

risk management, rely heavily on interest rate forecasts.Thus

financial economists, fixed-income managers, and investors

in general are interested in the ability to forecast the behavior

64 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/for Journal of Forecasting.2018;37:64–82.

CALDEIRA ETAL.65

of the term structure of interest rates. In addition to the uncer-

tainty with respect to which yield curve model to use, market

practitioners and policy makers also use these models as guid-

ance to different decisions. As argued by Pesaranand Skouras

(2002), purely statistical measures need not be directly rele-

vant to a particular decision maker, and the benefit of a model

is dependent not on its statistical accuracy but on its advantage

in a given decision environment.

In order to represent the real-time behavior of an investor

who wishes to use predictions of the yield curve to con-

struct a bond portfolio, it is important not only to take into

account the uncertainty surrounding his choice of models in

every time period, but also to describe how he learns about

the best-performing models. To this end, it is fundamental

to incorporate in the analysis the decision-making process in

which forecasts are to be used, since this environment will

define how the investor ultimately evaluates the performance

of alternative candidate models. This paper builds on the

purely statistical dynamic model averaging (hereafter DMA)

procedure developed by Raftery, Kárny, and Ettler (2010), to

develop an economically motivated algorithm to combine or

to select forecasts, such that combination weights reflect the

portfolio returns obtained by each individual model.

Raftery et al. (2010) use a Markov chain to model the

problem of real-time prediction under uncertainty regarding

the best forecasting model to use. More specifically, they

consider different state-space models characterizing eachpos-

sible model candidate, and represent unknown changes to the

data-generating process via a Markov chain. The resulting

predictive distribution of this system is a mixture with one

component for each model candidate. Thus the best predic-

tion is a weighted combination of the forecast of each model,

where weights are computed recursively based on the predic-

tive likelihood of the different models. However, to estimate

this system it is also necessary to estimate the state-space and

Markov chain models recursively, which is computationally

very demanding, and can restrict the number of alterna-

tive models. To circumvent this issue, Raftery et al. propose

approximating the original system using forgetting factors to

approximate this otherwise burdensome recursive estimation

procedure.

The approach of Raftery et al. (2010) is very much

related to adaptive forecast combination strategies used in

economics (see, e.g., Newbold & Harvey, 2002; Granger

& Jeon, 2004). In fact, Pesaran and Timmermann (2007)

argue that forecast combination strategies are well suited

to deal with model uncertainty, and use it to account for

unknown structural breaks. Moreover, Pesaran and Timmer-

mann see forecast combinations as a strategy to diversify risk

in the face of model uncertainty. Additionally, Pesaran and

Timmermann (2000) document how the best models to

forecast stock returns change over time, and argue that it

does not seem plausible that the real-time search for return

predictability will be conducted using only one model.

Koop and Korobilis (2012) use the DMA approach of Raftery

et al. (2010) to forecast inflation, and argue that it might be

better to use only the model with highest predictive probabil-

ity in tas the period-t+1 forecasting model. The rationale for

trimming forecast is to avoid giving weights to models that

perform poorly and add noise to forecasts of period t(Granger

& Jeon, 2004). Koop and Korobilis labeled their approach

dynamic model selection (hereafter DMS).

The literature on forecast combination is largely based on

the use of purely statistical measures of forecast accuracy

to evaluate alternative models, and to determine combina-

tion weights (see Timmermann, 2006), for a survey on fore-

cast combinations). However, as pointed out by Granger and

Pesaran (2000), Pesaran and Skouras (2002), and Grangerand

Machina (2006), when forecasts are used in decision making

it is important to consider the decision process in the evalu-

ation of these forecasts, thereby maintaining the interaction

between the forecasting model and the decision-making task.

This is the approach of Carriero, Kapetanios, and Marcellino

(2012) and Xiang and Zhu (2013), who evaluate the economic

performance of different yield curve models in a bond port-

folio optimization setting. Nevertheless, these studies do not

take into account the uncertainty that surrounds the investor’s

choice of models at each point in time, and assume that the

same model is used throughout the entire evaluation period.

Trying to incorporate the advantages of forecast combinations

to alleviate model uncertainty and structural breaks while also

considering the decision-making task, Caldeira, Moura, and

Santos (2016b) evaluate the effectiveness of different yield

curve combination strategies in terms of an economic crite-

rion. Although Caldeira et al. evaluate the economic benefits

of forecast combination strategies, all combination schemes

considered were constructed using only measures of statis-

tical performance, ignoring the ultimate use of the forecasts

when computing combination weights.

The economically motivated forecast combination

approach developed here incorporates the desire of an

investor to profit from the return predictability through the

incorporation of a gain function based on portfolio returns.

To assess the benefits of the proposed forecast combination

scheme, an optimal bond portfolio application is considered,

in which nine different specifications of yield curve models

can be used to forecast bond returns. Specifically,we consider

the canonical Gaussian dynamic term structure of Joslin,

Singleton, and Zhu (2011), the dynamic Nelson–Siegel

model of Diebold and Li (2006), and its arbitrage-free version

proposed by Christensen, Diebold, and Rudebusch (2011).

Moreover, we also consider three alternative factor dynamics

for these models: VAR, AR, and a diagonal VAR, where

correlation among factors is allowed through the covari-

ance matrix of contemporaneous shocks, but not through

dependence on lagged values of other factors.