Interest rate structured products: can they improve the risk–return profile?

Abstract

In this paper, we investigate the contribution of interest rate structured bonds to portfolios of risk-averse retail investors. We conduct our analysis by simulating the term structure according to a multifactor no-arbitrage interest rate model and comparing the performance of a portfolio consisting of basic products (zero-coupon bonds, coupon bonds and floating rate notes) with a portfolio containing more sophisticated exotic products (like constant maturity swaps, collars, spread and volatility notes). Our analysis, performed under different market environments, as well as volatility and correlation levels, takes into account the combined effects of risk premiums required by investors and fees that they have to pay. Our results show that capital protected interest rate structured products allow investors to improve risk–return trade-off if no fees are considered. With fees, our simulations show that structured products add value to the basic portfolio in a very limited number of cases. We believe our paper contributes to understanding the role of structured products in investors portfolios also in light of the current regulatory debate on the use of complex financial products by retail investors.

Keywords:

• Structured products
• efficient frontier
• portfolio diversification
• interest rate derivatives
• term structure model

JEL:

• G11
• G17
• E47

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Given the term structure of discount factors, we compute the simple forward rates with starting dates being the coupon reset dates and as final date the coupon payment date. Given we have different coupon dates, we consider the average forward rate.

2 For the sake of completeness, the dynamics of the two factors, under the new measure are $\begin{array}{rl}\mathrm{d}x\left(t\right)& =a\left(\frac{-{\lambda }_1\sigma }{a}-x\left(t\right)\right)\mathrm{d}t+\sigma \mathrm{d}{W}_1\left(t\right),x\left(0\right)=0,\\ \mathrm{d}y\left(t\right)& =b\left(\frac{-{\lambda }_2\eta }{b}-y\left(t\right)\right)\mathrm{d}t+\eta \mathrm{d}{W}_2\left(t\right),y\left(0\right)=0.\end{array}$Under the true measure, the two factors will now revert to $-{\lambda }_1\sigma /a$ and $-{\lambda }_2\eta /b.$ Depending on the sign of ${\lambda }_i$, these long-run values can be negative, null or positive. In addition, the deterministic function $\varphi \left(t\right)$ is no longer the unbiased forecast of the future instantaneous rate.

3 Given that the number of simulations is very large, there is no significant difference in using the biased or the unbiased estimate of the covariance matrix. In addition, given the fact that we are using log-returns, notice that the fees do not affect the variances and the covariances. For this reason we omit the dependence of the covariance matrix on g.

4 In practice, $m_{high}=\frac{\sum _{j=1}^P{\mu }_{j,g_j}{1}_{{\mu }_{j,g_j}>0}}{\sum _{j=1}^P{1}_{{\mu }_{j,g_j}>0}}$ and $m^{low}$ is the expected return on the portfolio that solves $min\frac{1}{2}{\mathbf{w}}^{\mathrm{\prime }}\mathbf{V}\mathbf{w}$, sub ${\mathbf{1}}^{\mathrm{\prime }}\mathbf{w}=1$ and $\mathbf{w}\ge \mathbf{0}$ whilst $m^{high}=\underset{j=1,\dots ,P}{max}{\mu }_j$, i.e. the largest element in $\mu$. If all the products have a negative expected return, we set $m_{high}$ equal to the average expected returns of the best three products.

5 Notice that the utility function is defined in terms of log-returns. This is equivalent to adopt a power utility $u\left(x\right)=\frac{x^{1-\gamma }-1}{1-\gamma }$ defined on the terminal wealth, i.e. $W_0{e}_p^R$ and by setting $\lambda =-(1-\gamma )$.

6 The perfect fit at initial time between model and market zero-coupon bonds is possible if the following restriction is satisfied (1) ${\int }_t^T\varphi \left(s\right)\mathrm{d}s=-\ln \frac{P^{mkt}\left(0,T\right)}{P^{mkt}\left(0,t\right)}+\frac{1}{2}\left(V\left(0,T\right)-V\left(0,t\right)\right),$(1) By taking the partial derivative with respect to T and assuming that the initial discount curve is given by the Nelson–Siegel parametric function, we obtain the expression in the main text.

7 See https://www.newyorkfed.org/research/data_indicators/term_premia.html

8 See https://www.unive.it/pag/39846

9 In those portfolios we do not consider the global minimum variance portfolio

10 An additional parameters setting, assuming that the term premium is zero has been considered, but not reported here.

11 Indeed, the term premium is a time average, whilst the expected return is computed over the full five-year period.

12 This is also proved in Appendix A.

13 In this table, we do not report the scenario related to negative rates, because we will deal with this case separately later on, due to the particular care we have to use in designing the different products.

14 The formula for the mean vector and covariance matrix are given in Brigo and Mercurio (2006).

Additional information

Notes on contributors

Gianluca Fusai

Gianluca Fusai is Full Professor at Università Del Piemonte Orientale. Gianluca's research interests focus on Financial Engineering, Numerical Methods for Finance, Portfolio Selection, and Energy Markets. Gianluca has published extensively on these topics and has co-authored the textbook ‘Implementing Models in Quantitative Finance’ (Springer Finance).

Giovanni Longo

Giovanni Longo is researcher at Università del Piemonte Orientale where is teaches derivatives pricing and portfolio theory. His main research interests are structure products pricing, portfolio theory and market transparency.

Giovanna Zanotti

Giovanna Zanotti is Full Professor of Banking and Finance at Università degli Studi di Bergamo where she teaches Derivatives and Investments. She graduated and she had her Phd at Bocconi University. Her main research interests are structured products, derivatives and market efficiency.