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This assignment is structured in two chapters. Firstly, a summary of foreign exchange products: FX forwards, FX futures, FX options and currency swaps. Secondly, drawbacks and limitations of the Markowitz portfolio theory.
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 Date: 20170717
 Author: Raúl Bartolomé Castro
 Program: Distance Learning MBA
 Module: International Financial Management
Description
Table of Contents
2 Drawbacks and Limitations of the Markowitz Portfolio Theory 5
2.2 Financial Markets Correlation 5
5.1 Introduction to MeanVariance Portfolio Theory 11
List of Tables
Table 1 Summary of Foreign Exchange Products 4
Table 2 Summary of Drawbacks and Limitations of the Markowitz Portfolio Theory Foreign Exchange Products 7
Foreign Exchange Products
FX Forwards
FX forward are legally binding contracts, usually with a bank, to buy or sell an amount of foreign currency for a specific exchange rate at certain time in the future. They don’t require money up front. The closed of the contracts usually is settle on T+2 on cash or delivery basis. The contracts are overthecounter (OTC) and do not trade on an Exchange (Gandolfo 2016, p. 22; Investopedia 2017; Societe Generale 2017).
FX Futures
FX futures are legally binding contracts to buy or sell a standard amount of foreign currency for a specific exchange rate at certain time in the future. The contracts are established with the Exchange, usually with a central counterparty clearing house (CCP) that assumes most of the credit risk. They don’t require money up front. The can be closed any time before expiration (Eiteman, et al. 2016, p. 202; Gandolfo 2016, p. 29; Investopedia 2017).
FX Options
FX options are legally binding contracts that can be sold or bought. Two types:
 Call option that grants to the buyer (the holder of the option) the right to purchase a currency at specified price at expiration date or earlier^{[1]}.
 Put option, the complementary to the call option, that grants to the buyer the right to sell a currency at specified price at expiration or earlier.
The buyer needs to put money up front to purchase the option, so called premium. The contracts usually are traded in an Exchange. They are regulated and standardized by strike price, maturity date of the underlying assets (Eiteman, et al. 2016, p. 205; Federici & Gandolfo 2016, p. 49).
Currency Swaps
Currency swaps are legally binding contracts between two companies to exchange cash flows in different currencies for an agreed period. The cash flow usually proceeds from a corporate loan, at the beginning of the currency swaps the counterparties exchange the principal of the loan. During the duration of the contract they exchange the interest payment. At maturity, they exchange back the principals to revert the initial transaction (Eiteman, et al., 2016, p. 247; Investopedia, 2017).
Summary
Table 1 presents a summary of previous discussion.
Table 1 Summary of Foreign Exchange Products
FX Forwards 
FX Futures 
FX Options 
Currency Swaps 

Money up front 
No 
No 
Premium 
Principal 
Operations 
Buy Sell 
Buy (long) Sell (short) 
Buy (long) call Buy (long) put Sell (short) call Sell (short) put 
Exchange of principals and interest 
Traded 
OTC (bank) 
Exchange 
Exchange or OTC 
OTC (swap dealer) 
Contract fees 
Bank’ charges (bid/offer spread) 
Broker’ charges 
Broker’ charges 
Swap dealer’s charges 
Closing contract 
Difficult (closed at expiration date) 
Easy (can be closed prior to delivery) 
Easy (can be closed prior to delivery) 
Difficult (closed at expiration date) 
Market 
Opaque (private transaction) 
Transparent (information publically available) 
Transparent (information publically available) 
Opaque (private transaction) 
Customized contract 
Yes (tailored to customer needs) 
No (standardized contract) 
No (standardized contract) 
Yes (tailored to customer needs) 
Regulation 
Low 
High 
High 
Low 
Financial instrument 
Derivative 
Derivative 
Derivative 
Derivative 
Underlying asset 
Currency 
Currency 
Currency 
Currency 
Drawbacks and Limitations of the Markowitz Portfolio Theory
Improbable Events
Taleb (2001) defines the black swan theory. A black swan even is characterized by (i) rarity, a shocking event, (ii) extremeness, an event with mayor relevance and (iii) retrospective predictability, understanding the event after it happened, rationalized by hindsight.
He argues that modern portfolio theory (MVPT) is not better than its inputs, does not predict securities prices and only minimizes risk in terms of variance for an expected return. Taleb supports a portfolio where the investors protect the portfolio to extreme and improbable black swan evens rather than expected (Eiteman, et al., 2016, pp. 526727).
Financial Markets Correlation
Identification of securities with low correlation is key to take full advantage of MVPT, this is sometimes difficult to achieve. Markets present strong correlation on extraordinary events such as terrorist attack on September 11, 2001 or global financial crisis in 2018 (Eiteman, et al., 2013, p. 471) and the correlation is growing over decades due to global financial connection (Eiteman, et al., 2013, p. 475).
Transaction Cost
MVPT does not consider the impact of transaction cost for the portfolio diversification, especially significant in emerging markets. Kaira et al. (2004) preformed a study of low correlation markets to USA market considering different weights of securities allocation. They concluded that only a small allocation of 10% in international markets may be justified and even so, this advantage might disappear once the taxation is incorporated.
Investor Utility
An expected utility function is a proxy for investor preference for expected return. MVPT is consistent utility maximization in terms of mean and variance (Markowitz, 1959, pp. 205211). However, the normal distribution is not acceptable in a realistic scenario, consequently not consistent with expected utility maximization (Michaud & Michaud, 2008, pp. 2223).
Estimation Errors
MVPT is prone to errors due to the optimization problem is very sensitive to perturbation in the input parameters often resulting in error maximization and investment irrelevant portfolios (Michaud & Michaud, 2008). Alternatives to MVPT are linear programming portfolio optimization (BenTal & Nemirovski, 1998) or robust optimization (Goldfarb & Iyengar, 2003) providing stable returns despite of big changes in markets (Platanakis & Sutcliffe, 2017).
Normal Distribution
Markowitz models the return of securities with a normal distribution, however this is insensitive to qualities of some securities like (i) fattailed and skewed returns, (ii) timevarying and clustered volatility and (iii) uncorrelated serial returns. Hu & Alec (2010) and Aas & Haff (2006) demonstrate that a Student t and Skewed t distribution capture more efficiently such events and provides better optimized efficient frontier.
Multiperiod Framework
MVPT was defined as a singleperiod investment, effective for short periods of time up to one year; however institutional investors have longterm investment horizon up to few decades (Michaud & Michaud, 2008, p. 24). The MVPT is extended to Nperiod generalization by Steinbach (1999), Frauendorfer & Siede (2000) and Elton, et al. (2014, pp. 237238) giving more complexity to the theory.
Other Views of Risk
Markowitz considers risk as volatility or variance, however Xia (2015) highlights alternatives to measure risk in portfolio management:
 Value at risk (VaR) a statistical technique to calculates the amount and probability of potential loss (Elton, et al., 2014, p. 234; Investopedia, 2017).
 Kelly criterion (J.L. Kelly, 1956), that defines a mean logarithmic growth formula for optimal size of bet series (Piotrowski & Schroeder, 2007).
 Semivariance, where only returns below the mean are considered in the variability estimation (Michaud & Michaud, 2008, p. 20).
 Or simply the maximum loss that the investor is willing to take.
Summary
Table 2 presents a summary of MVPT limitations.
Table 2 Summary of Drawbacks and Limitations of the Markowitz Portfolio Theory Foreign Exchange Products
Item 
Description 
1 
It does not protect against improbable black swan events, 
2 
based on historical data that doesn’t guarantee future returns, 
3 
challenging to identify uncorrelated markets due to financial globalization, 
4 
excludes transaction and taxation cost, 
5 
might not represent investor utility function, 
6 
prone to errors due to input sensitivity, 
7 
insensitive to fattailed and sked returns, 
8 
difficult to adapt for multiperiods and 
9 
others measure of risk such as VaR, Kelly criterion, semivariance or maximum acceptable loss. 
References
Leung, P.L., Ng, H.Y. & Wong, W.K., 2012. An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment. European Journal of Operational Research, Volume 222, pp. 8595.
Aas, K. & Haff, I. H., 2006. The Generalized Hyperbolic Skew Student’s tDistribution. Journal of Financial Econometrics, 4(2), p. 275–309.
BenTal, A. & Nemirovski, A., 1998. Robust Convex Optimization. Mathematics of Operations Research, 23(4), pp. 769805.
Elton, E. J., Gruber, M. J., Brown, S. J. & Goetzmann, W. N., 2014. Modern Portfolio Theory and Investment Analysis. 9th Edition ed. New York: Wiley.
Eiteman, D. K., Stonehill, A. I. & Moffett, M. H., 2013. Multinational Business Finance. Edinburg: Pearson.
Eiteman, D. K., Stonehill, A. I. & Moffett, M. H., 2016. Multinational Business Finance. Global ed. Edinburg: Pearson.
Federici, D. & Gandolfo, G., 2016. International Finance and OpenEconomy Macroeconomics. 2nd Edition ed. Rome: Springer.
Frauendorfer, K. & Siede, H., 2000. Portfolio Selection Using Multistage Stochastic Programming. Central European Journal of Operations Research, 7(4), pp. 277 – 289.
Gandolfo, G., 2016. International Finance and OpenEconomy Macroeconomics. 2nd Edition ed. Rome: Springer.
Hu, W. & Alec, K. N., 2010. Portfolio optimization for Student t and skewed t returns. Quantitative Finance , 10(1), pp. 91105.
Investopedia, 2017. Currency Futures. [Online]
Available at: http://www.investopedia.com/terms/c/currencyfuture.asp
[Accessed 18 June 2017].
Investopedia, 2017. Currency Swaps. [Online]
Available at: http://www.investopedia.com/examguide/cfalevel1/derivatives/currencyswaps.asp
[Accessed 25 June 2017].
Investopedia, 2017. Value At Risk – VaR. [Online]
Available at: http://www.investopedia.com/terms/v/var.asp
[Accessed 09 July 2017].
Investopedia, 2017. What is a ‘Currency Forward’. [Online]
Available at: http://www.investopedia.com/terms/c/currencyforward.asp
[Accessed 18 June 2017].
Iyengar, G. & Goldfarb, D., 2003. Robust portfolio selection problems. Mathematics of Operations Research, 28(1), pp. 138.
Kaira, R., Sloichev, M. & Sundaram, S., 2004. Diminishing gains from international diversification. Financial Services Review, Volume 13, pp. 199213.
Markowitz, H., 1952. Portfolio Selection. The Journal of Finance, 7(1), pp. 7791.
Markowitz, H. M., 1959. Portfolio Selection. Efficent Diversification of Investments. New York: Cowles Fundation.
Michaud, R. O. & Michaud, R. O., 2008. EFFICIENT ASSET MANAGEMENT A Practical Guide to Stock Portfolio Optimization and Asset Allocation. Second Edition ed. New York: Oxford University Press.
Platanakis, E. & Sutcliffe, C., 2017. Asset–liability modelling and pension schemes: the application of robust optimization to USS. The European Journal of Finance, 23(4), p. 324–352.
Piotrowski, E. & Schroeder, M., 2007. Kelly criterion revisited: optimal bets. THE EUROPEAN PHYSICAL JOURNAL, Volume 57, p. 201–203.
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Steinbach, M. C., 1999. Markowitz Revisited: SinglePeriod and MultiPeriod MeanVariance Models. KonradZuseZentrum fur Informationstechnik Berlin, pp. 9930.
Taleb, M. N., 2001. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. London: Texere.
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Acronyms
CCP. central counterparty clearing house
MPT. modern portfolio theory
MVPT. meanvariance portfolio theory
OTC. overthecounter
VaR. value at risk
Appendices
Introduction to MeanVariance Portfolio Theory
Markowitz (1952) in “Portfolio selection” defines the meanvariance portfolio theory (MVPT), a pillar for modern portfolio theory (MPT). MVPT focuses in future performance and the selection of securities in the portfolio. It assumes that investors are only willing to increase the risk (variance or standard deviation) if the chances of higher portfolio returns are higher. The theory demonstrates that investors can optimize the relationship portfolio return and variance by selecting low correlated securities and optimum mix of the securities in the portfolio (Eiteman, et al., 2016, p. 526; Michaud & Michaud, 2008, p. 3; Leung, et al., 2012)

This is the definition of American options. European options, that are the minority, can be exercised at expiration date only. ↑
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