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Review of Derivatives Research
Published in:

23-07-2020

Diversification with options and structured products

Authors: Shuonan Yuan, Marc Oliver Rieger

Published in: Review of Derivatives Research | Issue 1/2021

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Abstract

Different from diversification of stocks, there are two strategies to diversify portfolios consisting of options: one is to combine options on single underlying stocks, and the other one is to buy an option based on the index of these stocks. In this paper we analyse which diversification strategy is optimal for classical rational investors with constant relative risk aversion. We employ the Black–Scholes model and the stochastic volatility model of Heston for generating the processes of underlying stocks as well as pricing the derivatives. The results are developed first for options and then extended to some important classes of structured financial products: capital protected notes, discount certificates and bonus certificates. We find that investors’ choices on the two diversification strategies differ noticeably, but in general for convex payoffs index options are preferable, whereas for concave payoffs a portfolio of single stock options has usually higher utility.
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Footnotes
1
Empirical studies typically find a premium of overpricing of about 0.5% for simple products on large markets, but average values are as high as 8% in other situations. Some single products can have even larger mispricing.
 
2
See Branger and Schlag (2004) for example.
 
3
Since our aim is the comparison of derivatives on different underlying stocks ceteris paribus, we do not search for the optimal fraction of the wealth in derivatives nor the exposure of the optimal portfolio to different risk factors for the retail investor.
 
4
This corresponds to the uncapped capital protection (1100) according to the SVSP Swiss Derivative Map.
 
5
Sometimes called Low Exercise Price Option (LEPO), basically the underlying without dividend payments.
 
6
This allows a comparison with Hens and Rieger (2014).
 
7
The parameter properties of the Heston model have been estimated by a large number of studies, and the estimated parameters may differ from paper to paper. Our chosen parameters are in the generally agreed region as basically in line with Liu and Pan (2003).
 
8
See Branger and Schlag (2004). The analytical solution would not exist even if each stock of the index followed a geometric Brownian motion and all the stocks were independent.
 
9
Summary of results is available upon request.
 
10
The predefined level refers to the nominal protection level for the capital protected note, the limited profit potential (cap) for the discount certificate, and the conditional protection level for the bonus certificate if the barrier is not breached.
 
Literature
Benartzi, S., & Thaler, R. (1995). Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics, 110, 73–92.CrossRef
Benet, B. A., Giannetti, A., & Pissaris, S. (2006). Gains from structured product markets: The case of reverse-exchangeable securities. Journal of Banking and Finance, 30(1), 111–132.CrossRef
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.CrossRef
Blümke, A. (2009). How to Invest in Structured Products: A Guide for Investors and Investment Advisors. Burlington: Wiley.
Branger, N. & Breuer, B. (2008). The optimal demand for retail derivatives. Working paper.
Branger, N., & Schlag, C. (2004). Why is the index smile so steep. Review of Finance, 8, 109–127.CrossRef
Branger, N., Schlag, C., & Schneider, E. (2008). Optimal portfolios when volatility can jump. Journal of Banking and Finance, 32, 1087–1097.CrossRef
Breuer, W., & Perst, A. (2007). Retail banking and behavioral financial engineering: The case of structured products. Journal of Banking and Finance, 31, 827–844.CrossRef
Burth, S., Kraus, T., & Wohlwend, H. (2001). The pricing of structured products in the swiss market. Journal of Derivatives, 9, 30–40.CrossRef
Cao, J., & Rieger, M. (2013). Risk classes for structured products: Mathematical aspects and their implications on behavioral investors. Annals of Finance, 9, 167–183.CrossRef
Das, S. R., & Statman, M. (2013). Options and structured products in behavioral portfolios. Journal of Economic Dynamics and Control, 37, 137–153.CrossRef
Dichtl, H., & Drobetz, W. (2011). Portfolio insurance and prospect theory investors: Popularity and optimal design of capitalprotected financial products. Journal of Banking and Finance, 35, 1683–1697.CrossRef
Dimson, E., Marsch, P., & Staunton, M. (2006). The worldwide equity premium: A smaller puzzle. EFA 2006 Zurich Meetings Paper and AFA 2008 New Orleans Meetings Paper.
Driessen, J., & Maenhout, P. (2007). An empirical portfolio perspective on option pricing anomalies. Review of Finance, 11, 561–603.CrossRef
Eraker, B., Johannes, M., & Polson, N. (2003). The impact of jumps in volatility and returns. Journal of Finance, 58, 1269–1300.CrossRef
Fink, H., Geissel, S., Sass, J., & Seifried, F. T. (2019). Implied risk aversion: An alternative rating system for retail structured products. Review of Derivatives Research, 22(3), 357–387.CrossRef
Gollier, C. (2004). The economics of risk and time. Cambridge: MIT Press.
Helberger, D. (2012). Why do investors buy structured products? A behavioral finance explanation. The Journal of Wealth Management, 15, 51–60.CrossRef
Henderson, B., & Pearson, N. (2011). The dark side of financial innovation: A case study of the pricing of a retail financial product. Journal of Financial Economics, 100, 227–247.CrossRef
Henderson, B. J. & Pearson, N. D. (2007). Patterns in the payoffs of structured equity derivatives. AFA 2008 New Orleans Meetings Paper.
Hens, T., & Rieger, M. O. (2014). Can utility optimization explain the demand for structured investment products? Quantitative Finance, 14, 673–681.CrossRef
Heston, S. L. (1993). A closed form solution for options with stochastic volatility with applications to bonds and currency options. The Review of Financial Studies, 6, 327–343.CrossRef
Jones, C. S. (2006). A nonlinear factor analysis of s&p 500 index option returns. Journal of Finance, 61, 2325–2363.CrossRef
Liu, J., & Pan, J. (2003). Dynamic derivative strategies. Journal of Financial Economics, 69, 401–430.CrossRef
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
Rieger, M. O. (2012). Why do investors buy bad financial products? Probability misestimation and preferences in financial investment decisions. Journal of Behavioral Finance, 13, 108–118.CrossRef
Stoimenov, P. A., & Wilkens, S. (2005). Are structured products ’fairly’ priced? An analysis of the german market for equity-linked instruments. Journal of Banking and Finance, 29, 2971–2993.CrossRef
Vrecko, D., & Branger, N. (2009). Why is portfolio insurance attractive to investors. Working paper.
Wallmeier, M., & Diethelm, M. (2009). Market pricing of exotic structured products: The case of multi-asset barrier reverse convertibles in switzerland. The Journal of Derivatives, 17, 59–72.CrossRef
Wilkens, S., Erner, C., & Röder, K. (2003). The pricing of structuredproducts in germany. Journal of Derivatives, 11, 55–69.CrossRef
Metadata
Title
Diversification with options and structured products
Authors
Shuonan Yuan
Marc Oliver Rieger
Publication date
23-07-2020
Publisher
Springer US
Published in
Review of Derivatives Research / Issue 1/2021
Print ISSN: 1380-6645
Electronic ISSN: 1573-7144
DOI
https://doi.org/10.1007/s11147-020-09169-x

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