International Finance

Session 5 — Financial Institutions and Firms: International Portfolio Investment

Laura Contreras-Portela

KEDGE Business School

October 2026

One portfolio, twelve countries

Over 1980–2007, a US investor holding only US stocks earned 1.11% a month with a standard deviation of 4.25. The same investor, holding the optimal international portfolio, earned 1.40% with a standard deviation of 4.74.

• More return and more risk — so the comparison needs a measure that handles both at once.
• Adjusted for risk, the international portfolio wins in every one of the twelve countries studied.
• Today is about why that gain exists, how large it is, and what stops investors from taking it.

Open with the numbers rather than the theory, because the theory is easier to accept once they have seen the size of the prize.

A US investor who held only American shares earned one point one one percent a month. The same investor holding the best international mix earned one point four zero.

[ask] Is that better?

Do not accept yes. The standard deviation also rose, from four twenty-five to four seventy-four. More return and more risk is not obviously better, and that is exactly why we need a measure that puts the two together - which is where the Sharpe ratio comes in, in about ten minutes.

Then the second bullet, which is the one worth remembering: once you adjust for risk, the international portfolio beat the domestic one in all twelve countries in the study. Not most. All.

Last line sets up the session. Why does the gain exist, how big is it, and why does almost nobody take it.

Where we are

Sessions 3 and 4 went through the instruments. We now turn to the institutions that hold them, and the first question is how anyone should hold a portfolio at all.

Today:

1. International portfolio investment — risk reduction, the optimal portfolio, exchange-rate effects and the limits

Next session:

2. Mutual funds · 3. Muñoz (2020) · 4. Insurance · 5. Investment firms ·
3. Bank management · 7. Economic efficiency

One question runs through all of it: why does an intermediary exist at all? Everything an institution does, an investor could in principle do alone — so each institution has to earn its place.

Put the chapter in context before starting.

Two sessions on instruments: money markets, bonds, stocks, mortgages, currencies, derivatives. Today we change the question. Not what is the claim, but who holds it and why.

We only do section one today - international portfolio investment. The rest of the chapter, from mutual funds onwards, is next session.

[point at the key idea]

And give them the thread that runs through the whole chapter. Everything a mutual fund does, you could do yourself. Everything a bank does, a lender and a borrower could in principle arrange between themselves. So for each institution we meet, the question is what it does that you cannot do as cheaply alone. Today’s answer, for the international portfolio, is going to be: almost nothing - and yet people still do not do it.

Timing. This section needs about 90 minutes of its own:

• hook and roadmap 8
• correlations and the risk floors 15
• the Sharpe measure and the optimal portfolio 20
• Problem 5.1 15
• the efficient set, composition and the gains 17
• exchange rate and Problem 5.2 11
• other routes, Problem 5.3 and home bias 20

If it is sharing a session with the end of the chapter on securities markets, you have closer to 80 and need to lose about 25 minutes. Cut in this order: Problem 5.3, other ways to get there, and what the optimal portfolio holds. The argument still lands without them - hook, correlations, floors, Sharpe, optimal portfolio, 5.1, efficient set, gains, exchange rate, 5.2, home bias.

Do not cut Problem 5.1 or the home-bias slide. The first is the examinable mechanics and the second is the payoff the whole section is built towards.

1 · International portfolio investment

1 · Why diversification works

Portfolio risk falls as you add securities, but only because their returns do not move together. Correlation, not the number of holdings, does the work.

Average correlation of monthly stock returns, within a country (on the diagonal) and between countries:

	AU	FR	DE	JP	NL	CH	UK	US
Australia	0.586
France	0.286	0.576
Germany	0.183	0.312	0.653
Japan	0.152	0.238	0.300	0.416
Netherlands	0.241	0.344	0.509	0.282	0.624
Switzerland	0.358	0.368	0.475	0.281	0.517	0.664
United Kingdom	0.315	0.378	0.299	0.209	0.393	0.431	0.698
United States	0.304	0.225	0.170	0.137	0.271	0.272	0.279	0.439

Start from the mechanism, not the table.

Adding securities reduces risk only if they do not all move together. If every stock in your portfolio rose and fell as one, holding fifty would be no safer than holding one. So the thing that matters is correlation, and the number of holdings only matters through it.

[point at the diagonal]

The bold figures are the correlation between two stocks picked inside the same country. Everything below is the correlation between two different countries.

[ask] Compare the diagonal with the off-diagonal. What do you notice?

Every off-diagonal number is smaller. Two British stocks move together at nought point seven; a British and a Japanese stock at nought point two.

That is the whole case for international diversification in one table. You cannot escape the common factor inside one economy - the same interest rate, the same recession, the same government. Across economies, you partly can.

One detail if they ask: the US row is low all the way across, and its own diagonal is the lowest at nought point four four. A large, diverse economy provides more internal diversification than a small one - which also means a US investor has less to gain abroad than a Swiss investor does.

1 · How far risk falls

Keep adding stocks and risk falls — but only to a floor. What remains is systematic risk: the part no amount of diversification removes.

Three curves, same shape, three different floors.

[trace one curve with a finger]

Each one starts at the risk of holding a single stock and falls as you add more. Steeply at first - the second stock helps enormously - then barely at all. By about twenty holdings you have captured most of what is available.

[ask] Why does it flatten instead of going to zero?

Because some risk is common to every company in the set. A recession, a rate rise, a war. Diversification removes what is specific to one firm; it cannot remove what hits all of them. That remainder is systematic risk.

[point at the three dashed lines]

Now the point of the slide. The floor is not the same height. A Swiss investor diversifying only inside Switzerland stops at nought point four four. An American stops at nought point two seven - a bigger, more varied economy. Go international and the floor drops to nought point one two.

Say the consequence plainly: the gain from going abroad is largest for investors in small economies. A Swiss investor has far more to gain than an American one, which is a result you can predict from the correlation table we just looked at.

1 · Measuring performance

The world beta measures how sensitive a national market is to world market movements — the systematic part, which diversification cannot remove.

The Sharpe performance measure puts return and risk in one number: excess return per unit of total risk.

SHP_i = \frac{\bar R_i - R_f}{\sigma_i}

• \bar R_i — mean return of market i
• \sigma_i — standard deviation of those returns
• R_f — the risk-free rate (US Treasury bill)

Monthly, 1980–2007:

Market	Mean	SD	β	SHP
Sweden	1.67	7.11	1.17	0.168
Netherlands	1.35	5.19	0.99	0.167
United States	1.11	4.25	0.88	0.149
Hong Kong	1.54	8.77	1.06	0.121
France	1.20	6.00	1.04	0.121
Japan	0.92	6.53	1.10	0.067

Two measures, and they answer different questions.

Beta asks how much of a market’s movement comes from the world moving. A beta of one point one means that market amplifies world swings; below one, it damps them.

The Sharpe ratio asks something more practical: how much extra return did you get for each unit of risk you carried? Excess return on top, total risk underneath.

[point at the formula]

Note what is in the denominator - total risk, the standard deviation, not beta. That matters: Sharpe judges you on everything that moved, not only the part correlated with the world.

[point at the table]

Now read it with them, because the ranking is not the ranking of returns.

[ask] Hong Kong returned one point five four a month and the United States one point one one. Which was the better investment?

The United States, comfortably. Hong Kong’s standard deviation was eight seventy-seven against four twenty-five, so its Sharpe ratio is a third lower. High returns bought with high volatility are not a free lunch - they are a purchase.

And Japan at the bottom: the lowest mean return in the table, with high volatility. Nineteen eighty to two thousand and seven covers the bubble and the lost decade.

1 · The optimal portfolio

Investors prefer more wealth to less and dislike risk. With a risk-free asset available, the best portfolio of risky assets is the one that maximises the Sharpe ratio:

\max (SHP_{op}) = \frac{\bar R_{op} - R_f}{\sigma_{op}}

With two risky assets A and B:

\bar R_{op} = x_A \bar R_A + x_B \bar R_B

\sigma_{op} = \left[x_A^2\sigma_A^2 + x_B^2\sigma_B^2 + 2x_Ax_B\sigma_{AB}\right]^{1/2}

Substituting and maximising with respect to the weights gives

x_A = \frac{(\bar R_A - R_f)\sigma_B^2 - (\bar R_B - R_f)\sigma_{AB}} {(\bar R_A - R_f)\sigma_B^2 + (\bar R_B - R_f)\sigma_A^2 - (\bar R_A - R_f + \bar R_B - R_f)\sigma_{AB}}

x_B = 1 - x_A

Do not derive this. Explain what it is doing and then use it.

The investor can always put money in the risk-free asset, so the only question left is which mix of risky assets to hold. The answer is the mix with the best reward per unit of risk - the highest Sharpe ratio. That mix is the same for everybody, regardless of how brave they are; how brave you are only decides how much of your money goes into it rather than into Treasury bills.

[left column]

The portfolio return is just the weighted average of the two returns. The portfolio risk is not - and the third term in that bracket is why. The covariance term is what makes the whole thing work: if the two assets move against each other, that term is negative and the portfolio is less risky than either asset alone.

[right column]

This expression is what you get when you maximise the ratio with respect to the weights. It looks unpleasant and it is only algebra. In the exam you substitute numbers into it, which is what we are about to do.

[ask] Before we compute anything: look at the numerator. What makes the weight on A large?

A high excess return on A, a high variance on B, and a low covariance between them. All three say the same thing - hold more of the asset that contributes return and less of the one that duplicates risk you already have.

1 · Problem 5.1

For 1980.1–2001.12, monthly, in percent, for the US and Netherlands indexes:

\bar R_{US} = 1.26, \sigma^2_{US} = 19.62 · \bar R_{NL} = 1.38, \sigma^2_{NL} = 26.52 · R_f = 0.55 · \sigma_{US,NL} = 14.14

1. What is the optimal international portfolio?
2. What are its expected return and risk?
3. What is its Sharpe performance?
4. How does that compare with the US alone?

Ten minutes in pairs. Calculators out — this one is pure substitution, and it is the kind of question that appears on the exam.

Two things to flag before they start, because both cost marks.

The data gives you variances, not standard deviations. Nineteen point six two is a variance; the standard deviation is its square root, four point four three.

And the covariance is given directly, fourteen point one four. They do not need to build it from the correlation, although it is worth noting where it comes from: four forty-three times five fifteen times nought point six two.

[let them work, then take it on the board]

Excess returns first: US nought point seven one, Netherlands nought point eight three.

Numerator: nought seven one times twenty-six fifty-two, minus nought eight three times fourteen fourteen. Seven point zero nine.

Denominator: thirteen point three four.

So x_US is fifty-three percent and the Netherlands forty-seven.

[ask] The Netherlands has the higher return. Why is it not the bigger half?

Because it also has the higher variance, and the two markets are correlated at nought point six two, so the extra Dutch return does not buy much extra diversification.

Then the portfolio: return one point three two, standard deviation four point two nine, Sharpe nought point one seven nine.

And the comparison, which is the real answer to the question: the US alone had a Sharpe of nought point one six zero. Both markets individually are below the mix. That is diversification - the combination beats both of its parts, and nothing about either market changed.

Worked. Excess returns 0.71 and 0.83. Numerator = 0.71 x 26.52 - 0.83 x 14.14 = 7.09. Denominator = 0.71 x 26.52 + 0.83 x 19.62 - 1.54 x 14.14 = 13.34. x_US = 0.532, x_NL = 0.468. R_op = 1.316. Var = 18.40, SD = 4.29. SHP_op = (1.316 - 0.55)/4.29 = 0.179, against SHP_US = 0.160 and SHP_NL = 0.161.

1 · The efficient set, drawn

This is the picture the algebra was building towards, so take a minute on it.

[point at the crosses]

Each cross is one national market: its average monthly return against its standard deviation. Hong Kong far out on the right, high return and high risk. The United States bottom left, modest return and the lowest risk of the twelve.

[point at the OIP dot]

The dot is the optimal international portfolio for a US investor. One point four zero percent a month at a standard deviation of four point seven four.

[ask] Find a single country that is above and to the left of that dot.

There is none. Every individual market is worse - either less return for the same risk, or more risk for the same return. A combination of twelve things is better than any one of them.

[trace the line from the risk-free point]

The line starts at the risk-free rate and passes through the OIP. Its slope is the Sharpe ratio, which is the cleanest way to see what that formula was doing: of all the lines you could draw from the risk-free rate to some portfolio, the optimal one is the steepest.

[ask] And what are the points on the line between the risk-free rate and the dot?

Mixtures of Treasury bills and the optimal portfolio. Beyond the dot you are borrowing at the risk-free rate to hold more of it. Which is why the mix is the same for everyone and only the position along the line differs.

1 · What the optimal portfolio holds

For a US investor, the optimal international portfolio over 1980–2007:

Market	Weight
Netherlands	31.11%
Sweden	28.01%
United States	20.70%
Hong Kong	8.76%
Italy	6.60%
Australia	4.82%
Total	100%

Three things to notice:

• Only six of the twelve markets appear at all. The others add nothing once these are held.
• The investor’s own market is a fifth of the portfolio, not the whole of it.
• The weights are not proportional to market size. Sweden is a small market with a large weight, because its returns were high and only loosely correlated with the rest.

The composition differs by the investor’s domicile, because each investor’s home market is already in their portfolio.

[cuttable - the composition matters less than the fact that a gain exists]

Three things to draw out, and the third is the one that surprises people.

First, most markets get a weight of zero. The optimiser is not trying to own a bit of everything - it drops any market whose risk and return are already delivered by the ones it has kept.

Second, the US investor’s own market is one fifth of the portfolio. Remember that number, because at the end of the session we will see what investors actually hold, and it is nothing like twenty percent.

Third, and this is worth pausing on.

[ask] Sweden is a small economy. Why is it twenty-eight percent of the portfolio?

Not because it is big - weights here have nothing to do with market capitalisation. Sweden had the highest Sharpe ratio in the table and its returns were not closely tied to the others. High reward per unit of risk, and risk that does not duplicate what you already carry.

Last line: the table on the original slide has a different column for each investor’s country, because a Dutch investor already holds Dutch assets in a way an American does not. The optimal portfolio depends on where you start.

1 · The size of the gain

One line per country. The grey dot is what that country’s investors got holding only their own market; the orange dot is the optimal international portfolio for them. The gap is the gain.

[ask] Which country gains the most, and can anyone say why before I tell you?

Japan, by a long way - from nought point zero six five to nought point one seven seven, nearly three times. Japanese investors spent this period in a market with poor returns and high volatility, so almost anything else was an improvement.

[point at the top of the chart]

And the smallest gain is the Netherlands, which already had one of the best domestic Sharpe ratios in the sample. The pattern is general: the worse your own market, the more you gain by leaving it.

[pause]

Now the line that matters more than any individual country.

Every single bar points the same way. Twelve countries, twelve gains, no exceptions. Whatever your starting point, the risk-adjusted performance improved by going international.

[ask] So why is this not what everybody does?

Hold that - it is the last slide of the session.

1 · The exchange rate comes with it

A US resident investing abroad earns the foreign return and whatever the currency does:

R_{i\$} = R_i + e_i + R_i e_i \qquad \text{since} \qquad 1 + R_{i\$} = (1+R_i)(1+e_i)

where R_i is the local-currency return and e_i the change in the exchange rate — positive when the foreign currency appreciates against the dollar.

The currency affects risk through three separate channels:

Var(R_{i\$}) = Var(R_i) + Var(e_i) + 2\,Cov(R_i, e_i) + \Delta Var

its own volatility, its covariance with the local market, and the cross-product term.

The point of this slide is that a foreign investment is two bets, not one, and students routinely forget the second.

You buy Japanese shares. Two things then determine what you end up with: what the shares do in yen, and what the yen does against your currency.

[point at the formula]

The multiplicative version on the right is the honest one - one plus the dollar return equals one plus the local return, times one plus the currency change. Expand it and you get the three terms on the left, of which the last is small and the one people drop.

[ask] If the exchange rate adds a second source of randomness, does foreign investing have to be riskier?

Not necessarily, and the key idea explains why. Look at the covariance term. If the currency tends to rise when the local market falls, that covariance is negative and the currency is partly cancelling the market - the two risks offset rather than add.

So currency risk is not automatically bad news. It is an extra term that can have either sign, and which sign it has is an empirical question for each market.

Worth adding: this is also why the bond slide later says exchange risk makes international bond diversification hard. In a bond portfolio the local return is small and steady, so the currency term dominates everything.

1 · Problem 5.2

A US resident has just sold shares in a British firm. The shares returned 15% in pounds, over a period in which the pound depreciated 5% against the dollar.

What is the dollar return, in percentage terms?

Two minutes. It is a one-line calculation and the point is the third term.

[ask] First, without computing: will the dollar return be above or below fifteen percent?

Below. The pound fell, so each pound you bring home buys fewer dollars.

[ask] And is it exactly ten percent?

That is the trap, and most of the room will say yes. Fifteen minus five is ten, and ten is wrong.

[do it on the board]

One plus fifteen percent, times one minus five percent. One point one five times nought point nine five is one point zero nine two five. So nine point two five percent.

Or in the additive form: fifteen, minus five, minus nought point seven five. That last term is the cross-product - the currency loss applies to your investment gains as well as to your original stake.

[pause]

Three quarters of a percent sounds trivial. Make the numbers bigger and it is not: a fifty percent return with a thirty percent currency fall loses you fifteen points to the cross term alone.

Worked. R$ = (1.15)(0.95) - 1 = 9.25%. Additive: 0.15 - 0.05 + (0.15)(-0.05) = 0.15 - 0.05 - 0.0075 = 9.25%.

1 · Other ways to get there

International bonds. Less studied than equities, and exchange risk makes the gains hard to realise — though currency forwards can hedge most of it away.

International mutual funds. Diversification bought at home: no extra transaction or information costs, no legal barriers, and professional managers.

Country funds. Invest in a single foreign market — useful for building your own allocation, or for reaching markets otherwise closed.

ADRs. Foreign shares repackaged to trade on a US exchange, in dollars.

ETFs. Track a foreign index and trade like a single stock.

Hedge funds. Privately pooled, aggressive and flexible — leverage, short positions, derivatives, across currencies, bonds, stocks, commodities and property. Sought for absolute returns, whether markets rise or fall, with the risk that entails.

[cuttable - name international mutual funds in one line and move on]

Do not read six boxes aloud. Group them and make one point.

Everything here is a different route to the same destination: foreign exposure without personally opening a brokerage account in Tokyo.

[left column, briefly]

Bonds first, and note the honest caveat - with bonds the currency term swamps the return term, so the diversification gain is harder to collect unless you hedge it with the forwards from last session.

Then funds, which are the practical answer for almost everybody: one purchase, at home, in your own currency.

[right column]

ADRs they have already met, in the stock market section. ETFs are the modern version of the same idea - buy an index as if it were one share.

Hedge funds are the odd one out and worth flagging as such. The others buy diversification. Hedge funds promise absolute return, which is a different product with a different risk, and we come back to them next session.

[ask] If international mutual funds make this so easy, what is left of the excuse for not diversifying?

Nothing - which is exactly the puzzle of the next slide.

1 · Problem 5.3

US-based international mutual funds, against the S&P 500 and the US MNC index, monthly over 1977–1986:

	Mean return	SD	\beta_{US}
US-based international mutual funds	1.58	5.78	0.69
S&P 500	1.17	4.25	1.00
US MNC index	1.34	4.38	0.98

What is your analysis of their relative performance?

The US MNC index holds the 60 US multinationals with the highest share of international revenue.

[cuttable - 5.1 already tests the mechanics; this one tests judgement]

Five minutes in pairs. There is no single number to compute, which is the point - this one tests whether they can reason with the measures rather than apply them.

[ask] Start with the easy observation. Which has the highest return?

The international funds, one fifty-eight against one seventeen. But by now they should not stop there.

[ask] So divide by risk. Return per unit of standard deviation?

Funds, nought point two seven three. S&P, nought point two seven five. MNC index, nought point three zero six. The funds’ advantage in raw return almost exactly disappears once you account for how much more they moved - and the MNC index beats both.

[point at the beta column]

Now the interesting column. The funds have a beta of nought point six nine against the US market, while both US portfolios sit at about one.

[ask] What does that tell you?

That the funds really did hold something different. They were genuinely less exposed to US market movements - that is international diversification showing up in the data.

[pause]

Then the conclusion worth writing down, and it has two halves.

The funds delivered real diversification, visible in the beta. But they did not deliver better risk-adjusted performance than simply holding American multinationals - firms that earn abroad and so carry foreign exposure inside a domestic share.

[ask] So is buying an international fund worth the fees?

On this evidence, debatable. You can get part of the exposure at home. It is a genuinely open question and a good one to leave with them.

1 · Why almost nobody does it

Home bias. Investors hold far more domestic equity than any model recommends. Four explanations are offered:

• Domestic securities provide services foreign ones do not, such as hedging domestic inflation.
• Barriers, formal and informal — legal, administrative, transaction and information costs, taxes.
• The prudent man rule: institutions may simply be forbidden to hold more than a set fraction abroad.
• It may be fading, as markets integrate and country funds and international mutual funds spread.

Large-cap bias. Portfolios that do go abroad concentrate in large firms — and large firms are the worst vehicle for the job.

• Large caps are typically multinationals, with foreign customers and investors, so their returns are driven by common global factors and are highly correlated.
• Small-cap firms are driven by local factors, so they are the more effective instrument for international diversification.

Close the session on the puzzle.

We have spent an hour establishing that international diversification improves risk-adjusted performance in every country studied, and that it is easy and cheap to obtain. So:

[ask] Why does the average investor hold ninety percent of their money at home?

Let them try before you give the list. The four explanations are on the slide and none of them is fully convincing, which is worth admitting - home bias is still an open puzzle in the literature.

Take the second and third seriously, because they are the testable ones. Barriers are real but have fallen enormously, and home bias has not fallen nearly as fast. The prudent man rule is real and binding for pension funds, but it does not explain household behaviour.

[right column]

Then the second bias, which is subtler and a nice one to finish on.

Suppose you do invest abroad. You will almost certainly buy large, familiar, listed companies - Toyota, Siemens, Nestlé.

[ask] What is wrong with that?

Those are exactly the firms whose returns are driven by the same global factors as your own large caps. You have bought a foreign label on a correlated asset.

The firms that would actually diversify you are the small, locally oriented ones you have never heard of - and those are the hardest to buy.

Leave them with that: the easiest foreign investment to make is the one that diversifies you least.

Next session

Session 6 continues the chapter: mutual funds, the Muñoz (2020) reading, insurance companies, investment firms, bank management and economic efficiency.

Read Muñoz (2020) on the boards of socially responsible mutual funds before the session. The discussion is assessed.

Press O for the slide overview · C to draw · S for speaker notes · F for fullscreen · E then print for a PDF of the slides.

That is the whole of international portfolio investment.

Next session is the rest of the chapter, and it is mostly institutions: mutual funds, insurance companies, investment banks and brokers, how a bank actually manages its balance sheet, and then the asymmetric-information material - adverse selection, moral hazard, conflicts of interest.

One thing to bring. Read Muñoz. It is on socially responsible mutual funds and how their boards affect performance, and it picks up directly from today’s material, since a mutual fund is how most people will ever hold the portfolio we spent today constructing.

Say plainly that the discussion is assessed, the same way the green bonds one was.