I am doing a series on portfolio management strategies in the hope that it would lead to some Excel tools for the same. In the **first part** on portfolio diversification, we looked at correlations between equity and debt, equity and gold, large cap and mid/small cap.

In this post, let us consider the correlation between Indian stocks and international stocks.

**CNX 500 vs S&P 500(US)**

Let us first compare the Indian broad-based index, CNX 500, with S&P 500 a large cap index of 500 US stocks. The correspondence between the indices may be far from perfect but is good enough for our purposes.

The correlation coefficient for these two indices is only **0.57**.

The correlation between six-month returns is **0.52.**Thus only **27% **(0.52 x 0.52 = R-squared) of the returns are correlated.

Thus, on the face of this evidence, it makes a lot of sense to allocate a ‘small’ portion of the portfolio to US stocks!

Wait a minute! What about currency risk?

Yes, currency exchange rate is a crucial component of investing in international stocks. We shall consider currency risk after we look at a couple of indices.

**CNX 500 vs S&P 350 (****Europe****)**

“The * S&P Europe 350*® is an equity index drawn from 17 major

*markets, covering approximately 70% of the region’s market capitalization.” –*

**European****us.spindices.com**

Between 28 July 2000 and 20^{th} June 2014, the correlation between CNX 500 and S& P 350 six-month returns is **0.71. **Thus **51% **(0.71 x 0.71 = R-squared) of the returns are correlated.

Therefore, can we safely add some European stocks in our folio?

What about the correlation between US and European stocks? That is important if I already have US stocks in the folio.

For the same duration, the correlation between six month returns of S&P500 (US) and S&P 350 (Europe) is **0.88. **Thus a good **79% **(0.88 x 0.88 = R-squared) of the returns are correlated.

So the moment we have 3 different types of stocks, be it from different regions as here, or of different market cap (as seen in part I), we have a problem.

It is not easy to decide how much of each type should be in the folio.

We have what is known as a **correlation matrix**

| S&P 500 |
| |

| 1 | 0.59 | 0.71 |

| 0.59 | 1 | 0.88 |

| 0.71 | 0.88 | 1 |

It is easy to understand why the diagonal entries are all ‘1’. The correlation of an index with itself must be ‘1’!

We will consider such matrices in the future and learn how to construct optimized portfolios with them.

For the moment the message is, stocks from different regions across the globe are poorly correlated. This means that by including international stocks in the portfolio, the overall diversification should improve and the volatility will be lowered.

For example, when we had a sideways market just a little while ago, Sensex increased only by 2.6% bet Dec. 11 2009 to Aug. 31st, 2012, the S&P 500 increased by approximately 29%.

So folios with US stocks in them would have fared much better than those with only Indian stocks.

This is because of the poor correlation between the two markets. Although individually US and Indian stocks are risky, as part of a well diversified folio, they bring the down the overall risk.

This is the key concept behind diversification. Risky securities poorly correlated with each other result in a less risky portfolio.

Let us find out if this statement holds true under more rigorous backing testing, taking into account, currency risk.

Before we do that, CNX 500 has correlation **0.93** with MSCI Asia (excluding Japan) – it is a mix of securities from China, Hong Kong, India, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan, and Thailand. Thus, about **88% **returns are correlated.

Other MSCI indices can be tracked from **here**

Read this **paper** for more data on correlations among indices the world over.

** ****Currency Risk**

The following discussion is based on, ** Modern Portfolio Theory & Investment Analysis**, by E. J. Elton, M. J. Gruber, S. J. Brown and W N. Goetzmann

To understand currency risk, let us consider a US investor and an Indian investor who buy the same US stock at a price of 40 USD. To keep things simple, let us ignore expenses involved in this purchase for both parties.

After 1 year, the stock price is 50 USD.

The return for the US investor (R_{US}) can be calculated from

50 = 40 x (1+ R_{US}) or

1+R_{US} = (50/40)

**R _{US} = 25%**

The return for the Indian investor (R_{Indian}) would depend on the exchange rate at the time of purchase and time of redemption (or valuation)

If the rate was Rs. 45 per dollar during purchase and Rs. 55 per dollar after an year,

(55 x 50) = (45 x 40) x (1+ R_{Indian}) or

1+R_{Indian} = (55 x 50)/ (45 x 40) = (55/45) x ( 50/40)

**R _{Indian }=52.8%**

Here (55/45) = 1+R_{X} (this gives the % change in the currency rate or the *exchange return*)

(50/40) = 1+ R_{US }(the % change in the stock price as above)

1+R_{Indian} = (1+ R_{US}) x (1+R_{X})

Notice that the return for the Indian investor, depends on, R_{X}, the exchange return.

In the above case, exchange rate at the time of valuation is higher than the rate upon purchase.

Therefore, the Indian investor would have obtained a higher return than the US investor would.

If the exchange rate had decreased, the Indian investor would have obtained a lower return that his/her US counterpart.

For example, if the rate was Rs. 55 per dollar during purchase and Rs. 45 per dollar after an year,

1+R_{Indian} = (45 x 50)/ (55 x 40) = (45/55) x ( 50/40)

**R _{Indian} = 2.27%**

Notice the extraordinary difference in returns due to currency fluctuations alone!

Thus, the exchange rate determines the quantum of return. This additional source of volatility is known as currency risk.

**Indian citizen investing in US stocks**** **

Let us understand how this risk plays out for an Indian investor who wish to hold US stocks. For this study we,

- consider historical monthly exchange rates from
**here** - shall use monthly MSCI US index data. “The MSCI USA Index is designed to measure the performance of the large and mid cap segments of the US market. With 609 constituents, the index covers approximately 85% of the free float-adjusted market capitalization in the US” –
**msci.com** - shall compute 1-year and 10-year rolling returns

**1-year rolling returns**

**US**** citizen investing in US stocks: ** average return = 8.5%; standard deviation (risk) = 17.2%

**Indian citizen investing in US stocks: **average return = 14.6%; standard deviation (risk) = 21.3%

The extra risk for the Indian investor originates from the volatility in the exchange rate.

Is the Indian investor is taking on more risk by investing in US stocks?

The average 1Y return for the BSE Mid-Cap is 22%; standard deviation (risk) = 41%

Thus compared to Indian mid-cap stocks, the risk for the Indian investor in US stocks over a period of 1 year is close to 50% lower!

**10-year rolling returns**

**US**** citizen investing in US stocks: ** ** ** average return = 8.3%; standard deviation (risk) = 4.9%

**Indian citizen investing in US stocks: **average return = 15%; standard deviation (risk) = 9.1%

Again, the extra risk for the Indian investor originates in the volatility in the exchange rate

Notice how the Indian investor got more returns than the US investor when the exchange rate kept increasing (leftmost black line). When the increase reversed (middle black line), returns for the Indian investor, sharply fell down.

The average 10Y return for the BSE Mid-Cap is 14.4%; standard deviation (risk) = 3.1%

Therefore, this implies that over longer periods, the risk associated with investing in US stocks is about 3 times higher (9.1% vs 3.1%) for the Indian investor compared to an investment in regional (Indian) stocks.

This is again due to the exchange rate risk.

I find this statistic troubling. I will need to dig around more to understand more

**US citizen investing in Indian stocks**

Let us understand how this risk plays out for a US investor who wish to hold Indian stocks. For this study we,

- consider historical monthly exchange rates from
**here** - shall use monthly MSCI India index data. “The MSCI India Index is designed to measure the performance of the large and mid cap segments of the Indian market. With 69 constituents, the index covers approximately 85% of the Indian equity universe.” –
**msci.com** - shall compute 10-year rolling returns

**10-year rolling returns**

**Indian citizen investing in Indian stocks: ** average return = 11.1%; standard deviation (risk) = 6.1%

**US**** citizen investing in Indian stocks: **average return = 9.2%; standard deviation (risk) = **7.3%**

Had the US investor put money in the MSCI USA index, he would have got an average return of 8.3%; standard deviation (risk) = **4.9%** (as mentioned above)

Thus, the US investor also faces a higher risk by investing in Indian stocks. However, the risk is still less than 2 times (7.3% vs 4.9%) compared to an investment in regional (US) stocks.

*The exchange risk affects the Indian investor in US stocks much more than the **US** investor in Indian stocks.*

As mentioned earlier, I find this statistic troubling.

The key questions are,

**Does international diversification lower overall portfolio risk without improving returns? Or, does it provide higher portfolio returns at higher risk?**

Technically speaking, we are yet to answer these questions. We will need to perform an *efficient frontier analysis* to answer this question. I am trying to develop an automated Excel sheet for this. Therefore, we will consider this question in the coming weeks.

**My Take: **I have always believed in diversification through international equity. It is nothing more than a belief for me as it ‘seemed’ to make sense.

About 4% of my retirement folio consists of international equity, a little more than 1% of which is US stocks (FT US feeder fund) and rest from PPFAS Long Term Value Fund (LTVF).

Thus, it is too small, and I have not held them long enough to tell if it has made a difference to my portfolio.

While I am certainly not going to reduce my international equity allocation to zero, I am also not in a flaming hurry to increase it either. I will wait until I get the efficient frontier analysis tool ready and answer the above questions.

I recently posted on **risk adjusted return numbers** for PPFAS LTVF and found that risk was considerably lower than the CNX 500, which is most likely to arise from its well-diversified portfolio with international stocks.

Meanwhile, if you are convinced about holding a small percentage of international equity, funds like Templeton India Equity Income and/or PPFAS LTVF provide good international equity exposure with tax-free long term capital gains, since they contain more than 65% Indian equity, unlike feeder funds, which are taxed like debt funds.

Apologies for being inconclusive about diversification with international stocks. Unfortunately it requires further analysis.

In the next part of this portfolio diversification series, we will consider correlation among sectors.

Superb methodology to make us understand the concept with real data & numbers. Amazed by the work you do and skill you possess ! By FT US feeder fund….do you mean….FT India Feeder Franklin US Opportunities Fund ??? As of today PPFAS LTV has 11.44% of Equity in Greater Europe. Is it worthwhile to figure in Index of the Region to see the effect ?

Superb methodology to make us understand the concept with real data & numbers. Amazed by the work you do and skill you possess ! By FT US feeder fund….do you mean….FT India Feeder Franklin US Opportunities Fund ??? As of today PPFAS LTV has 11.44% of Equity in Greater Europe. Is it worthwhile to figure in Index of the Region to see the effect ?

If you have data since 1982, then you should compare with the corresponding data from Sensex/BSE Midcap if available. And are these data with or without reinvested dividends?

Secondly, the currency fluctuatations and Indian indices have a high degree of correlation, because FII are becoming a predominant player in the Indian markets.

In Part II, you can explore if portfolio rebalancing between Nifty / BSE Midcap / BSE 200 and a S&P 500 / MSCI USA provides a better risk-adjusted return or not. That would be the real-world simulation. This is the way you would be investing in future.

Just thinking about standard deviation as the lone indicator of Risk is not the best thing.

This is data without reinvested dividends.

Yes, correlation with the currency is high. I will post more details on this in another post. Will try and include portfolio rebalancing as well.

Yes the standard deviation aloe is not not good enough. Agreed. Will try and find out how the efficient frontier analysis plays out with and without international equity.

If you have data since 1982, then you should compare with the corresponding data from Sensex/BSE Midcap if available. And are these data with or without reinvested dividends?

Secondly, the currency fluctuatations and Indian indices have a high degree of correlation, because FII are becoming a predominant player in the Indian markets.

In Part II, you can explore if portfolio rebalancing between Nifty / BSE Midcap / BSE 200 and a S&P 500 / MSCI USA provides a better risk-adjusted return or not. That would be the real-world simulation. This is the way you would be investing in future.

Just thinking about standard deviation as the lone indicator of Risk is not the best thing.

This is data without reinvested dividends.

Yes, correlation with the currency is high. I will post more details on this in another post. Will try and include portfolio rebalancing as well.

Yes the standard deviation aloe is not not good enough. Agreed. Will try and find out how the efficient frontier analysis plays out with and without international equity.

Great article but I think currency risk is unpredictable over long term unlike equity.Also would like a correlation between sensex 30 and dow jones ( a set of 30 stocks).The basic premise of diversification across geographies is somewhat achieved even if i invest in sensex i.e index fund because sensex 30 contains some companies which operate in global market.The IT,pharma pack (Infy,TCS,Sun pharma etc) specially,automobile to some extent and commodities through common international commodity price(cos like tata steel,hindalco etc).In a globalised world a companies country of listing need not be its sole market.Cos like samsung,honda etc have global revenue streams.In fact 70% of S&P 500 earnings is ex US.Would like to know what has been the correlation between major world indexes in last 3-4 years to get a clearer picture.

That is a great point. Will post this correlation in the next couple of days.

studied some data in s&p website http://us.spindices.com/indices/equity .In last 3 yrs bse sensex has returned 12.22% cagr and s&p 500 cagr of 17.83% as on june 30.Hmm…thats around 5% outperformance by s&p ,well wait its not really an index outperformance ,this is the period when rupee got slammed from around 45 to 60,well around 16-17% in 3 years.So the gap can be explained by currency movement alone.Thats a preety strong correlation leaving aside currency movement.

Yes that is a good point. I will need post more about this correlation soon. Thanks.

Great article but I think currency risk is unpredictable over long term unlike equity.Also would like a correlation between sensex 30 and dow jones ( a set of 30 stocks).The basic premise of diversification across geographies is somewhat achieved even if i invest in sensex i.e index fund because sensex 30 contains some companies which operate in global market.The IT,pharma pack (Infy,TCS,Sun pharma etc) specially,automobile to some extent and commodities through common international commodity price(cos like tata steel,hindalco etc).In a globalised world a companies country of listing need not be its sole market.Cos like samsung,honda etc have global revenue streams.In fact 70% of S&P 500 earnings is ex US.Would like to know what has been the correlation between major world indexes in last 3-4 years to get a clearer picture.

That is a great point. Will post this correlation in the next couple of days.

studied some data in s&p website http://us.spindices.com/indices/equity .In last 3 yrs bse sensex has returned 12.22% cagr and s&p 500 cagr of 17.83% as on june 30.Hmm…thats around 5% outperformance by s&p ,well wait its not really an index outperformance ,this is the period when rupee got slammed from around 45 to 60,well around 16-17% in 3 years.So the gap can be explained by currency movement alone.Thats a preety strong correlation leaving aside currency movement.

Yes that is a good point. I will need post more about this correlation soon. Thanks.

Thanks Vinay. Sorry for the late response. Yes I am referring to that feeder fund from Franklin. Index of the region could play a role but PPFAS just have a few such stocks and only 1/2 stocks from a region so not sure about it.

Thanks Vinay. Sorry for the late response. Yes I am referring to that feeder fund from Franklin. Index of the region could play a role but PPFAS just have a few such stocks and only 1/2 stocks from a region so not sure about it.

Dear Pattu, the source of exchange rate is not provided.

“consider historical monthly exchange rates from here”

Not working as no linking is there.

Thanks

Ashal

Thanks Ahsal. This is the link. Updated the post.

http://www.forecasts.org/data/data/EXINUS.htm

Dear Pattu, the source of exchange rate is not provided.

“consider historical monthly exchange rates from here”

Not working as no linking is there.

Thanks

Ashal

Thanks Ahsal. This is the link. Updated the post.

http://www.forecasts.org/data/data/EXINUS.htm

For international diversification does it make sense for an NRI with no taxable income in India to invest in US feeder fund of Franklin which are treated as debt fund as you said in the post ? Did you create that excel sheet for "efficient frontier analysis tool " (I dont know that that means) ?

For international diversification does it make sense for an NRI with no taxable income in India to invest in US feeder fund of Franklin which are treated as debt fund as you said in the post ? Did you create that excel sheet for "efficient frontier analysis tool " (I dont know that that means) ?

Brilliant, would love if you could include MOST NASDAQ 100 also