the impact of currency choice on minimum variance portfolios€¦ · eur loc usd jan-00 jan-01...

The Impact of Currency Choice on Minimum Variance Portfolios

Quantitative Equity Research

Date: November 2015

2 | HSBC Global Asset Management

Executive Summary: The Impact of CurrencyChoice on Minimum Variance Portfolios

Base Currency and Portfolio CompositionIn this paper we explore the effects of choice of base

currency in Minimum Variance portfolio optimisation

and find that choice of currency significantly affects

final portfolio composition. Contrary to recent papers

referenced later, we conclude however that investors

should use USD returns in their optimisation

regardless of their base currency.

Currency BiasesChanging the optimisation currency increases the

proportion of stocks denominated in that base currency

selected for the optimal portfolio. We look at regional

portfolio allocations when optimisation currency

changes. As expected, the optimised portfolio

becomes skewed towards countries which share

the same base optimisation currency.

Volatility and ReturnsWe find that there appears to be no material difference

in final risk and return outcomes, despite the fact that

the underlying portfolios change considerably.

What may an investor do?Minimum Volatility strategies are often benchmarked

against capitalisation-weighted market portfolios,

using risk-adjusted performance metrics. It follows

therefore that the choice of base currency greatly

affects the resultant minimum variance portfolio.

However, research illustrates that there seems to be no

material difference in overall portfolio volatility from

changing the optimisation currency. In our opinion,

investors should consider using USD-optimised

portfolios because the resultant portfolio follows

more closely the broad structure of the capitalisation-

weighted market portfolio – and this is less risky if

correlation structures were to become more unstable.

HSBC Global Asset Management | 3

IntroductionIn this note, we explore the effects of changing the currency of

optimisation when constructing Minimum Variance Portfolios

(MVP). This issue has been explored by Jourovski (2011)1 and

also by Analytic Investors (2014)2, with both sets of authors

coming to different conclusions. This is a very important topic

because the choice of base currency in the optimisation has a

fundamental effect on the resulting portfolios.

Why should we care about the base currency when

constructing the Variance-Covariance matrix used for

Minimum Variance optimisation? In multi-country universes,

we expect our choice of base currency to have a sizeable

impact on estimated individual stock variances and

covariances (Figure 1 shows that FX volatility is rather

significant when compared to equity volatility).

Figure 1: FX Volatility vs USD Benchmark Volatility (Annualised)

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In mathematical notation, the variance of a stock returns

denominated in USD would be:

For example, a stock in a country with a volatile FX/

USD rate and not too negative covariance between stock

return and FX/USD rate will have a higher volatility in USD

than if it were in a country with currency pegged to the

USD. Correspondingly, this will have an effect on all the

components of the overall Variance-Covariance matrix.

In the case of minimum variance optimisation, the impact

on the Variance-Covariance matrix will affect the results.

1 Alexei Jourovski, Unigestion, 2011, Currency Impact on Minimum Variance Portfolio.

2 Analytic Investors, 2014, Minimum Variance Strategies and Implications for Managing Currency Exposure (A Study of the MSCI Minimum Volatility Indices).

Of course, changing the base currency can reverse this. In this

paper, we conduct an empirical exercise examining the effects

of constructing MVP by changing optimisation currency.

For an optimisation using local currency, the stock returns

used in calculating the Variance-Covariance matrix are

calculated based on the listing currency of each stock, so a

portfolio will simultaneously have returns in multiple currencies

as an input into the optimisation. We construct our portfolios

using our in-house approach for constructing Global Low

Volatility portfolios, which initially screens for the top 300

stocks which are in line with our Value and Profitability core

process and then conducts a Minimum Variance optimisation

using a stock covariance matrix that has been cleaned and

covariance-shrunken to enhance stability.

Source: Factset, currency data between Jan 1991 and Jan 2015, MXWD data between Dec 1998 and Jan 2015.

σstock in USD = σstock in local FX + σFX/USD+ 2ρstock in local FX,FX/USD σstock in local FX σFX/USD

2 2 2


Figure 2: Number of Stocks in MVP using different base currencies

MethodologyFor our live Lower Volatility portfolios, we currently use

USD returns as the base currency for optimisation. The

reason for that is simple; the US has always had the largest

weight within the MSCI All Country World Index, having

a weight of 51.74% as of February 2015. Therefore, it

would be a natural decision to construct the portfolio in

the dominant currency. However, the problem becomes

slightly more complex when the investor is for example

a European investor, who wishes to receive his returns in

EUR. The investor might have 3 options for currency used

in optimisation- 1) USD, 2) EUR or 3) Local currency.

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Portfolio CharacteristicsWe start by looking at the number of stocks within each

portfolio. We see that the number of stocks is more or

less similar in the three portfolios.

Figure 3: % Overlap in names within EUR-USD portfolios and Local-USD portfolios

Source: Factset, IBES, Worldscope as at 31/01/2015.

Source: Factset, IBES, Worldscope as at 31/01/15.


3 Ledoit and Wolf (2004), “Honey, I shrunk the Sample Covariance Matrix”, Journal of Portfolio Management.

We now consider how much overlap we observe with each

portfolio by looking at the proportion of overlapping names

out of the total unique names in the portfolios. There is on

average a 37% overlap between the names of the MVP in

EUR and USD and a 46% overlap between the names of

the MVP in local currency and USD. It is clear that choice of

currency has a significant impact on the covariance matrix,

resulting in very different MVP. This comes as no surprise

to us as the entire covariance matrix changes when using

different base currencies.

However, despite the low overlap between names in each

portfolio, the style characteristics of the portfolios appear to

be similar. It is to be noted that the high positive exposures

to Value and Profitability are a consequence of our initial

EVROIC screening process.

Figure 4: Average Style Exposures (Minimum Average Portfolio)

USD Local EUR

Value 0.25 0.30 0.27

Quality 0.42 0.40 0.37

Volatility -0.79 -0.78 -0.73

Momentum 0.04 0.04 0.03

Size -0.63 -0.61 -0.61

Leverage -0.11 -0.03 -0.08

Trading Activity -0.16 -0.22 -0.19

Dividend Yield 0.35 0.40 0.39

Growth -0.20 -0.17 -0.18

Earnings Variability -0.05 -0.05 -0.03

Source: Factset, IBES, Worldscope, average exposures between Jan 2000 and June 2015.


It follows that we would expect the ex-ante volatility

of these portfolios to be similar.

Figure 5 looks at regional allocations based on returns

currency. We sort the top 10 currencies based on regions and

put the remainder under others (note we do not sort others

into regions). When the global MVP is constructed using

EUR as a base currency, we find that the average allocation

to stocks in EUR is substantially higher than that of the USD

portfolio 18% vs 5%. This is to be expected, in unexceptional

circumstances, stocks denominated in EUR will appear to

be the least relatively risky/volatile of the lot, as the currency

risk in EUR-denominated stocks would have been stripped

out due to our choice of base currency. We also see higher

weights to currencies that are very closely tied to the EUR,

Figure 5: Top 10 currencies of MVP and BenchmarkBenchmark

Other 24%

USD-linked 49%

Europe 27%

USD

Other 33%

USD-linked 49%

Europe 18%

USD-optimised

USD

EUR-optimised

Other 33% USD-linked

38%

Europe 29%

Local-optimised

Other 42%

USD-linked 38%

Europe 20%

CHF-optimised

Other 34%

USD-linked 39%

Europe 27%

JPY-optimised

Other 40% USD-linked

41%

Europe 19%

GBP-optimised

Other 34%USD-linked 38%

Europe 28%

like the CHF (if we exclude recent volatility). With the

objective of Minimum Variance portfolio construction being

to pick stocks which in combination minimise overall volatility,

it is natural that the ‘lower volatility’ EUR-denominated stocks

are more attractive and given higher weights in the EUR-

optimised portfolios.

Similarly, when we compare the USD portfolio to that of the

Local currency portfolio, we see that the USD portfolio has

a higher average weight in USD-denominated stocks; with

an average allocation of 43% vs 38% in the Local currency

portfolio (see Figure 5). However, it should be noted that

the USD-optimised portfolio still has a lower weight in the

USD-denominated stocks than the MSCI All Country World

benchmark, as well as the selection of the top 300 ranked

stocks, while on the other hand the EUR-optimised portfolio

has a higher weight in EUR-denominated stocks than the

MSCI All Country World benchmark and the top 300 stocks.

In February 2006, the MVP EUR-optimised had 2.13x the

MSCI All Country World benchmark’s weight in EUR-

denominated stocks. It is vital for an investor to decide if he/

she is comfortable with having such a significant overweight

position. On the other hand, the maximum that the USD-

denomination skew goes to is 1.22x in December 2006.



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CAD CHF TWD HKD MAD

Figure 6: Top 10 currencies of USD MVP Figure 7: Top 10 currencies of EUR MVP

Figure 8: Top 10 currencies of Local MVP Figure 9: Top 10 currencies of CHF MVP

Figure 10: Top 10 currencies of JPY MVP Figure 11: Top 10 currencies of GBP MVP

The figures above extend our analysis to a few other

currencies, namely CHF, JPY and GBP and as anticipated;

we see a weight bias towards currency of optimisation.



Portfolio Volatility and ReturnsHaving described the country and stock characteristics

of the portfolios, we now proceed to look at the risk and

return characteristics of the portfolios. MVP optimised

from returns in different currencies have different country

and stock allocations, it is important to investigate how this

would affect final portfolio outcomes. To start off, we have to

choose the currency we wish our returns to be generated in.

We also assume that our portfolios are unhedged. This is in

line with HSBC’s views on currency hedging of equities.

Currency choice has an impact on both returns and volatilities,

even at the benchmark level, as can be seen from Figure 12.

It can be seen that an investor that buys a EUR-denominated

MXWD benchmark will have lower volatility and returns than

an investor that buys a USD-denominated index. We do not

discuss the Local currency portfolios as we assume all returns

will be converted to the currency of choice.

Figure 12: MSCI ACWI Benchmark Risk-Return in USD, Local currency, EUR and JPY (Jan 2000 – Jun 2015)

USD Local EUR JPY

Annualised return 4.2% 4.0% 3.4% 5.1%

Annualised volatility 16.1% 14.3% 14.5% 19.0%

Sharpe Ratio 0.26 0.28 0.23 0.27

Source: Factset, MSCI as at 30/06/15 Returns are net of trading costs. Past performance should not be seen as an indication of future returns.

Now consider Minimum Variance optimisation using different base optimisation currencies. As can be seen from Figure 13, all

of HSBC’s MVPs have substantially lower average ex-post volatility than the MSCI All Country World benchmark. They also

have much higher Sharpe Ratios than the benchmark.

Figure 13: Annualised Volatility of MVPs under different optimisation currencies

USD Local EUR GBP JPY CHF

Portfolio Returns

currency

USD 10.0% 11.3% 11.2% 11.7% 10.2% 10.7%

EUR 10.2% 10.6% 9.7% 10.2% 10.2% 10.0%

JPY 12.7% 13.6% 13.4% 13.2% 12.5% 13.0%

Figure 14: Sharpe Ratio of MVPs under different optimisation currencies

USD Local EUR GBP JPY CHF

Portfolio Returns

currency

USD 1.16 0.95 0.99 1.00 1.00 1.07

EUR 1.04 0.92 1.05 1.06 0.91 1.04

JPY 1.01 0.88 0.92 0.98 0.91 0.97

Source: Factset, IBES, Worldscope as at 30/06/15 Returns are net of trading costs. Past performance should not be seen as an indication of future returns.


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Local-optimisation


Local-optimisation

As the overall aim of a Minimum Variance optimisation is to find

the set of portfolio weights which minimises estimated volatility

(ex-ante) and this should result in low realised volatility, we look

more closely at the ex-post volatilities of the resulting portfolios.

Here, there is little difference in ex-post volatility despite us having

constructed three very different portfolios. Looking more closely

at the rolling 3-year volatility in Figures 15 and 16, we can see that

there are periods where having USD as an optimisation currency

results in lower volatility than when using EUR as an optimisation

currency and vice versa. This is most probably because it is hard to

accurately estimate FX correlations and volatility to such accuracy.

Despite having an optimisation problem that aims to find the

portfolio of Minimum Variance relative to a particular currency, it

estimates volatility with large enough error such that the ex-post

volatility is not necessarily always lower than when using another

optimisation currency. We should note that with a rolling 3-year

volatility window, the ex-post volatility, regardless of optimisation

base currency, is lower than the cap-weighted benchmark.

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EUR-optimised MVP MXWD USD BenchmarkUSD-optimised MVP Local-optimised MVP

EUR-optimised MVP MXWD USD Benchmark

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Figure 16: 3-Year rolling ex-post volatility Portfolio in EUR

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Local-optimisation


Local-optimisation

Figure 18: Yearly returns Portfolio returns in EUR

Figure 15: 3-Year rolling ex-post volatility Portfolio in USD

Figure 17: Yearly returns Portfolio returns in USD

Even though our portfolio construction process is based on

Minimum Variance optimisation, there is a degree of alpha that is

included in the portfolio due to the stock ranking method used, thus

we are interested in observing the effect of optimisation currency

on portfolio returns. When looking at absolute returns, it is hard to

draw a clear conclusion either way. However, it is comforting to

note that the general pattern of returns appears to be rather similar

regardless of choice of optimisation currencies. For portfolios

where we convert returns to USD, USD-optimisation outperforms

EUR and Local currency optimisations in 6 out of 15 years of data,

EUR-optimisation outperforms for 4 years while Local currency

optimisation outperforms for the remaining 5 years. We see similar

results for portfolios where we convert returns to EUR, so there

seems to be no strong argument to support matching the currency

of optimisation to the currency of the portfolio’s final returns.

Figures 17 & 18 Source: Factset, IBES, Worldscope as at 31/12/2014 Returns are net of trading costs. Past Performance should not be seen as an indication of future returns.

Figures 15 & 16 Source: Factset, IBES, Worldscope as at 31/01/2015


Figure 19: Periods of outperformance Years of Outperformance (Optimisation Currency)

USD EUR Local

Returns CurrencyUSD 6 4 5

EUR 6 4 5

Source: Factset, IBES, Worldscope, Jan 2000 to June 2015

USD as a perceived ‘safe-haven’ currencyWe believe that the methodology of running Minimum

Variance optimisation with USD as a base currency is the

most appropriate one. Practically speaking, the USD has

historically been treated as a perceived ‘safe haven’ currency,

with many portfolios holding USD as a form of hedge

against equity market volatility. The idea behind the USD as

a perceived ‘safe haven’ currency is simply that when there

are crises, investors buy more USD, thereby hedging against

riskier assets that are held.

This can be seen on Figure 20, where we show the

correlations between the changes in the MSCI World Local

Currency Index and the nominal Effective Exchange Rate

(EER) from the Bank of International Settlement (BIS). These

EERs are geometric weighted averages of bilateral exchange

rates. We can see that the USD and JPY tend to have

negative correlations with equity market returns.

Figure 20: Periods of Outperformance

USD GBP AUD EUR JPY

Jan 1988 - Aug 2014 (0.14) 0.04 0.28 0.03 (0.18)

Jan 1999 - Aug 2014 (0.21) 0.00 0.41 0.15 (0.36)

When looking at this relationship through time, it clearly

demonstrates the USD’s role as a perceived ‘safe-haven’

currency, through its negative correlations with the market

especially during market crashes (note tech bubble and GFC

period). One could argue that the JPY has also provided this

behavior, though it has been more volatile recently.

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Figure 21: Time-varying correlation between USD and Equity Returns

Source: MSCI, BIS, data as at 31/08/2014.

Typically, MVP are known to be attractive to investors

because of their low drawdowns during times of crisis and

their comparative safety. Thus, from a practical perspective,

when looking at minimising volatility, we would also like to

seek to minimise volatility of a stock returns with respect to

that of a perceived ‘safe-haven’ currency.

Source: MSCI, BIS 31/08/2014. Returns are net of trading costs. Past Performance should not be seen as an indication of future returns.


ConclusionIn this note, we show the results of running the Minimum

Variance portfolio optimisation in USD, EUR, GBP, JPY, CHF

and local currency. Although the final risk and return metrics

appear to be rather similar, it is important to observe how

the choice of currency for optimisation fundamentally affects

portfolio composition. It is important to note that these

results are specific to our Minimum Variance construction

process and cannot be necessarily generalised for all MVP.

For investors looking to choose a base currency for

optimisation, it is important to be aware that running the

optimisation using a non-USD currency would most likely

result in an overall systematic overweighting of stocks in the

currency of choice. This is due to the nature of the Minimum

Variance optimisation, which incorporates the effects of

currency volatility on stock returns in the optimisation.

Practically speaking, we believe that an investor should

remain in USD-optimised portfolios as the US Dollar

maintains its perceived ‘safe haven’ currency status and

the resulting increased exposure to stocks denominated in

USD when choosing USD as the base optimisation currency

should certainly improve the safety of the portfolios.


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Figure 22: Yearly excess returns Portfolio returns in USD

Figure 23: Yearly excess returns Portfolio returns in EUR

Important Information

Appendix

For Professional Clients only and should not be distributed to or relied upon by Retail Clients.

The material contained herein is for information only and does not constitute investment advice or a recommendation to any

reader of this material to buy or sell investments.

This document is not intended for distribution to or use by any person or entity in any jurisdiction or country where such

distribution or use would be contrary to law or regulation. This document is not and should not be construed as an offer to sell

or the solicitation of an offer to purchase or subscribe to any investment.

Any views expressed were held at the time of preparation and are subject to change without notice. While any forecast,

projection or target where provided is indicative only and not guaranteed in any way. HSBC Global Asset Management (UK)

Limited accepts no liability for any failure to meet such forecast, projection or target.

The value of investments and any income from them can go down as well as up and investors may not get back the amount

originally invested. Where overseas investments are held the rate of currency exchange may also cause the value of such

investments to fluctuate. Investments in emerging markets are by their nature higher risk and potentially more volatile

than those inherent in some established markets. Stock market investments should be viewed as a medium to long term

investment and should be held for at least five years. Any performance information shown refers to the past and should not be

seen as an indication of future returns. Some of the ETFs invest predominantly in one geographic area; therefore any decline in

the economy of this area may affect the prices and value of the underlying assets.

To help improve our service and in the interests of security we may record and/or monitor your communication with us. HSBC

Global Asset Management (UK) Limited provides information to Institutions, Professional Advisers and their clients on the

investment products and services of the HSBC Group.

Approved for issue in the UK by HSBC Global Asset Management (UK) Limited, who are authorised and regulated by the

Financial Conduct Authority. Copyright © HSBC Global Asset Management (UK) Limited 2015. All rights reserved.

27503CP/ED/1015/FP15-1833 EXP 31/07/2016.

Source: Factset, IBES, Worldscope as at 31/12/2014 Returns are net of trading costs. Past Performance should not be seen as an indication of future returns.

the impact of currency choice on minimum variance portfolios€¦ · eur loc usd jan-00 jan-01...

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