Possibly The Worst Time to Invest

In my last blog post, I mentioned that I had recently set up a passive portfolio comprising 70% stocks and 30% bonds. You might wonder whether it is the worst time to invest, considering that the Dow Jones Industrial Average (DJIA) is near an all-time high while the Federal Reserves is planning to raise interest rates from an all-time low. Any fall in the DJIA will lead to losses on the stock component of the portfolio while any rise in interest rates will lead to losses on the bond component. While I do not welcome a crash in stock and/or bond prices, I am nevertheless comforted by the fact that there is a defence mechanism inherent in the portfolio, namely, portfolio rebalancing. When stock and/or bond prices undergo large changes, portfolio rebalancing will take advantage of such volatility and eventually lead to higher portfolio value. See the post on Volatility is Your Friend for more info.

Likewise, my other portfolios besides the passive portfolio mentioned above have defence mechanisms in place. My Supplementary Retirement Scheme (SRS) portfolio is based on Dollar Cost Averaging. Regardless of the price level of the unit trusts, a constant sum of money is invested in the portfolio every month. When prices are low, more units will be bought in, therefore reducing the average cost of the units. This defence mechanism has been tested and proven to work during the Global Financial Crisis in 2008. See the post on Dollar Cost Averaging Works Best with Volatile Stocks/ Unit Trusts for more info.

As for my active portfolio, it comprises preference shares and cash besides stocks and REITs. When the market crash comes, the preference shares will be liquidated and reinvested into beaten down stocks and REITs. Interestingly, this market timing strategy is also a form of portfolio rebalancing, except that it does not aim to maintain the same portfolio allocation throughout the market cycles. In fact, it is a more aggressive form of portfolio rebalancing, with the allocation to stocks increasing as the price of stocks gets lower and decreasing as the price of stocks gets higher. 

Of course, investing at the wrong time brings a lot of losses and heartaches. However, very few people can predict correctly where the market will move. Instead of waiting for the right time to invest, why not have the right strategy to invest with? Who knows, even when you have waited for the right time to invest, i.e. at the market bottom, you might not recognise that this is bottom or have the courage to invest.

There is a Chinese saying "运筹帷幄之中，决胜千里之外". If you plan your strategies properly, you could decide the outcome of a battle a thousand miles away. In investing, the equivalent concept is that the outcome of a battle is decided a thousand days away, before the market crash begins.

See related blog posts:

• Possible The Worst Time to Invest – A Year On
• Possibly The Worst Time to Invest – 2 Years On
• Possibly The Worst Time to Invest – 3 Years On
• Possibly The Worst Time to Invest – 4 Years On
• Possibly The Worst Time to Invest – 5 Years On
• Possibly The Worst Time to Invest – 6 Years On

The Passive Portfolio

This is the final part of the trilogy of blog posts on how I set up a passive portfolio. This trilogy was inspired by the desire to set up a portfolio that needs minimal attention. It is also to give an example to some of my friends who are new to investing on how they could invest their money.

Just to recap, in the first post, we discussed that a common rule of thumb for the allocation into the bond component of the portfolio is your age in percentage. For example, if your age is 30, you allocate 30% of your portfolio to bonds and 70% to stocks. We also discussed that the larger the margin allowed for volatility swings in the portfolio allocation before rebalancing takes place, the higher is the portfolio value. In the second post, we discussed that the greater the volatility of the stock and bond components, the higher is the portfolio value. Hence, based on the above research, my planning parameters for the portfolio are as follow:

Stock Allocation	70%
Bond Allocation	30%
Rebalancing Margin	8%

The bond allocation is actually lower than my actual age. That is because I am an aggressive investor. For less aggregate investors, they can stick to the rule of thumb mentioned above. For conservative investors, they can increase the allocation to bonds by 10% more than the rule of thumb suggests.

Next, on the selection of stocks that make up the stock component, I selected an index fund as literature overwhelmingly shows that the vast majority of investors actually cannot beat the market. There are 2-3 index funds available on unit trust platforms such as FundSuperMart (FSM) and DollarDex, namely, Infinity Global Stock Index, Infinity European Stock Index and Infinity US Stock Index. As the European and US funds are regional-specific, they have higher risk and volatility compared to the Global fund. Although the research above shows that higher volatility will lead to better portfolio value, my preference is for less country-specific risk to adverse events such as the European debt crises. Hence, my selection for the index fund is the Infinity Global Stock Index.

On the selection of bonds that make up the bond component, the research shows that bonds with long maturities and low coupon rates are most volatile and will lead to higher portfolio value. On this basis, the ideal bond would be the 30-year Singapore Government Securities (SGS) bond. Again, I deviated from my research for the following reasons (more excuses really):

• The SGS bond and the index fund are traded on different platforms. E.g. the SGS bond is traded on Singapore Exchange (SGX) or with the banks while the index fund is traded on unit trust platforms. When rebalancing takes place, you will need to transfer money across the platforms. The only platform that deals with both is FSM, but I don't like paying platform fees just for holding the bond/ funds.
• Because they are on different platforms, you will have to compute the current allocation to stocks/ bonds yourself. 
• The SGS bond can be traded on either SGX or with the banks. Bank staff seldom deals with SGS trading and you have to educate them every time you trade.
• The SGS bond reduces in maturity over time. Hence, every few years, the bond would have to be sold in exchange for new 30-year bond to maintain the long maturity.
• There is country-specific risk in SGS bonds.

Hence, I turned to FSM (but trade on DollarDex) for a selection of bond funds. A snapshot of the available list of bond funds is shown below.

Bond Funds Available at FSM

As mentioned in an earlier post on Why Unit Trust Expense Ratio Matters, expense ratios matter significantly in the overall return of the funds. At an expense ratio of 1% and possible returns from bonds of 5%, that is paying 20% of the expected returns for management of the funds every year. 

There are only a handful of bond funds that has expense ratio of around 1% or less. Among these bond funds, I selected the one with the higher risks, taking into consideration the fund size as well. My selection for the bond component is the Schroder ISF Global Corporate Bond SGD Hedged fund. According to the fund description on FSM, it is invested in bonds of governments, government agencies, supra-national and corporate issuers worldwide, with a maximum of 20% held in government bonds. Corporate bonds have higher risks than government bonds, which suits the objective of having a high-volatility bond, while reducing the country-specific risks with worldwide diversification.

Hence, my eventual portfolio is:

• 70% in Infinity Global Stock Index
• 30% in Schroder ISF Global Corporate Bond SGD Hedged fund
• Portfolio is rebalanced whenever the allocation exceeds the above allocation by 8%.

In the final analysis, research can tell you one thing, but the portfolio that you construct must be consistent with what you believe in, your risk appetite and your judgment of how financial markets will perform in future. You must be comfortable with the portfolio so that you can go through thick and thin with it. Only then can you reap the rewards of investing with the portfolio.

See related blog posts:

• Portfolio Rebalancing - A Fine Balancing Act 
• Volatility is Your Friend
• The Anti-Fragile Portfolios

Volatility is Your Friend

In the last blog post, we discussed the 2 questions on what should the allocation between stocks and bonds be and how frequent to rebalance. In this post, we'll discuss the next question on what type of stocks and bonds to buy. Again, we turn to sensitivity analysis to provide some clues on what type of stocks and bonds will provide the highest portfolio value. The assumptions in this sensitivity analysis is the same as those in the previous post, namely, an initial $10,000 is invested in a portfolio comprising 70% stock / 30% bond for 26 years since 1988, the stock component is invested in the Straits Times Index (STI) while the bond component is invested in an artificial Singapore Government Securities (SGS) bond created based on the present value of all coupons discounted at the longest SGS bond yield. The resultant portfolio is rebalanced whenever the allocation between the stock & bond components vary from the original allocation by 5%.

Since the bond is an artificially created one, we can vary the tenure and coupon rate to determine its impact on the final portfolio value at the end of 26 years. The portfolio values for each bond tenure (left column) and coupon rate (top row) are shown below. 

Figure 1: Highest & Lowest Portfolio Value at Different Bond Tenure & Coupon Rate

For each bond tenure, the portfolio that delivers the highest value is highlighted in green while the portfolio that delivers the lowest value is highlighted in orange. A few trends could be seen from this analysis. Firstly, most of the portfolios with the highest value occur at a coupon rate of 0% while most of the portfolios with the lowest value occur at the highest assumed coupon rate of 10%. Secondly, the longer the bond tenure, the higher is the portfolio value. These 2 observations could be explained by the fact that the lower the coupon rate and the longer the bond tenure, the more volatile is the bond. Figure 2 below shows the price of a high-volatility bond and a low-volatility bond as well as the value of 2 portfolios with these bonds. The high-volatility bond is a 30-year SGS bond with 3% coupon whereas the low-volatility bond is a 1-year SGS bond with 3% coupon.

Figure 2: Portfolio Value of High and Low Volatility Bonds

As shown in Figure 2, the low-volatility bond rarely changes in price, whereas the high-volatility bond fluctuates widely. The no. of times rebalancing takes place is 23 times for the low-volatility bond portfolio and 24 times for the high-volatility bond portfolio. It appears that the more frequent rebalancing, due to price changes of the bond component alone, adds to the final portfolio value.

Would the same conclusion be reached for volatility of the stock component? Here, we compare the performance of STI with FTSE. STI has an (geometric) average annual return of 5.0% over the last 26 years, which is very close to FTSE's 5.2%. However, STI has a standard deviation of 22.9% against FTSE's 14.6%. So, STI represents the high-volatility stock while FTSE represents the low-volatility stock. The performance of a portfolio with STI & a 1-year SGS bond with 3% coupon and FTSE & the same SGS bond is shown below.

Figure 3: Portfolio Value of High and Low Volatility Stock Indices

Again, the portfolio with the high-volatility stock index has a higher value than the portfolio with the low-volatility stock index. The no. of times rebalancing takes place is only 9 times for the low-volatility stock portfolio and 23 times for the high-volatility stock portfolio. Hence, due to price changes of the stock component alone, rebalancing takes place for an additional 14 times which adds to the final portfolio value.

What happens if we put both high-volatility stock and high-volatility bond (High / High) together in the same portfolio? The performance of the 4 portfolios of Low / Low, High / Low, Low / High and High / High are shown in Figure 4 below.

Figure 4: Portfolio Value of High and Low Volatility Stock Indices & Bonds

Not surprisingly, the best performance is the High / High portfolio, followed by the Low / High, High / Low and Low / Low portfolios. In terms of portfolio volatility, the High / High portfolio has the highest standard deviation, followed by the High / Low, Low / High and Low / Low portfolios. In terms of the no. of rebalancing, the High / High portfolio is rebalanced 24 times, 1 time more than the High / Low portfolio, 7 times more than the Low / High portfolio and 15 times more than the Low / Low portfolios.

Thus, from the above analysis, the more volatile the stock / bond components are, the higher is the final portfolio value with portfolio rebalancing. This is consistent with the concept that higher risk (volatility) leads to higher returns.

Finally, it should be noted that the above analysis is based on the historical price changes actually encountered. With a different price history, the results might be different.

See related blog posts:

• Portfolio Rebalancing - A Fine Balancing Act
• The Passive Portfolio
• Do Drawdowns Matter?

Portfolio Rebalancing – A Fine Balancing Act

I have been thinking about setting up a portfolio that needs minimal attention. In setting up the portfolio, a few questions come to mind, such as:

• What is the allocation between stocks and bonds?
• How frequent to rebalance?
• What stocks and bonds (or unit trusts) to buy?

On the first question, a common rule of thumb is to allocate to bonds your age in percentage. For example, if your age is 30, you allocate 30% of your portfolio to bonds and 70% to stocks. This rule of thumb is on the basis that the younger the person is, the more risk he can take. It is a sound rule of thumb.

On the second question, it is usual to rebalance the portfolio on a yearly basis. There is an alternative way of rebalancing the portfolio which is based on the amount of volatility the portfolio has gone through. For example, if the original portfolio allocation is 30% in bonds and 70% in stocks, the portfolio would be rebalanced only when the allocation deviates from the original allocation by say, a 5% margin.

To study the most optimal margin for rebalancing, I carried out back-testing based on the Straits Times Index (STI) and the longest Singapore Government Securities (SGS) bond yields for the last 26 years since 1988. An initial capital of $10,000 is assumed invested in the portfolio comprising of 70% stocks and 30% bonds. The stock component is assumed to be invested in STI while the bond component is assumed to be invested in a 10-year SGS bond carrying 3% coupon. This bond is an artificial bond computed based on the present value of all coupons discounted at the longest SGS bond yield. All dividends and coupons are ignored for this analysis. The portfolio values for each allocation (left column) and rebalancing margin (top row) at the end of 26 years are shown below.

Highest & Lowest Portfolio Value at Different Allocations & Rebalancing Margins

For each allocation, the portfolio that delivers the highest value is highlighted in green while the portfolio that delivers the lowest value is highlighted in orange. A few trends could be seen from this analysis. The portfolio with the lowest value tends to concentrate around the 0% rebalancing margin for all allocations except at very high or very low allocations, while the portfolio with the highest value tends to be parabolic, i.e. the portfolio with the highest value increases with increasing rebalancing margin until the margin reaches 9% before decreasing again.

On hindsight, it should not be difficult to explain these trends. With a high rebalancing margin, the stocks or bonds are allowed to run longer on their momentum before rebalancing takes place. For example, assuming stocks are on the rise, the stocks are allowed to run further before they are sold. This is consistent with letting your profits run. Conversely, if stocks are declining, they are allowed to decline further before the bonds are sold and invested in the stocks, hence, investors avoid catching a falling knife along the way down.

However, at very high or very low allocations, the optimal rebalacing margin reduces to around 5%. This is because a high rebalancing margin at these allocations means that the stocks or bonds need to go through very large changes before rebalancing takes place. For example, at 90% stock / 10% bond allocation, a 9% rebalancing margin would require bonds to rise or fall by 90% before rebalancing takes place. This is practically impossible, hence, the optimal rebalancing margin reduces at very high or very low allocations.

The figure above also shows what everybody knows, which is that portfolio allocation is an important factor in determining the final portfolio value. The higher the allocation to stocks, the higher is the portfolio value. However, between portfolio allocation and rebalancing margin, which has a higher influence? Based on the above case study, on average, a 1% increase in the allocation to stocks increases the portfolio value by $232. On the other hand, a 1% increase in the rebalancing margin increases the portfolio value by $101. So, portfolio allocation plays a more important role than the rebalancing margin in determining the final portfolio value. Nevertheless, the rebalancing margin can be used together with the portfolio allocation to enhance the portfolio value.

In practical terms, it should be highlighted that a high rebalancing margin would mean rebalancing only when stocks or bonds have undergone large changes. For example, with a 70% stock / 30% bond portfolio and rebalancing at 10% margin, with the STI at around 3,100 currently, rebalancing will only occur when the portfolio reaches either 80% stock / 20% bond or 60% stock / 40% bond allocation. Assuming the bond component does not change, the STI must rise to 5,300 points (71% rise) or drop to 2,000 points (36% drop) for rebalancing to take place. At a 5% rebalancing margin, the corresponding STI values are 4,000 points and 2,500 points.

Finally, it should be noted that the above analysis is based on the historical price changes actually encountered. With a different price history, the optimal rebalancing margin might be different. Nevertheless, the theory that it is better to rebalance less frequently to let your profits run or avoid catching a falling knife is still applicable.

Wishing everybody a Happy, Healthy and Prosperous Chinese New Year!


See related blog posts:

• Volatility is Your Friend
• The Passive Portfolio
• One Plus One Equals Two-and-a-Half

The Lost Art of Bond Investment

There are a couple of bonds and preference shares listed on the Singapore Exchange (SGX). Due to their scarcity, it is rare to find discussions on how these should be selected for investment. Last Christmas, I had the opportunity to reread the Security Analysis, written by Benjamin Graham and David Dodd. In it, there are 2 sections devoted to how bonds and preference shares should be selected for investment. It listed 2 criteria, namely, the minimum average earnings coverage and the minimum current stock value ratio.

The minimum average earnings coverage ensures that earnings are more than adequate to cover the fixed charges from bonds and preference shares for a sufficiently long period of time. The minimum current stock value ratio ensures that there is a sufficiently large pool of shares to cushion the bonds and preference shares in the event of financial distress. The values for the 2 criteria are listed as follows:

	Bonds	Preferred Stocks
Public Utilities	1.75x fixed charges	2x (fixed charges + preferred dividends)
Railroads	2x fixed charges	2.5x (fixed charges + preferred dividends)
Industrials	3x fixed charges	4x (fixed charges + preferred dividends)

Table 1: Minimum Average Earnings Coverage

	Bonds	Preferred Stocks
Public Utilities	$2 bonds to $1 stock	$1.5 (bonds & preferred) to $1 stock
Railroads	$1.5 bonds to $1 stock	$1 (bonds & preferred) to $1 stock
Industrials	$1 bonds to $1 stock	$1 (bonds & preferred) to $1.5 stock

Table 2: Minimum Current Stock Value Ratio

The reason for the more stringent requirements for preference shares compared to bonds is because preference shares have some contractual disadvantages. As an example, it is mandatory to pay bond coupons and principal as and when they fall due, failing which the company might enter into bankruptcy. In contrast, preference dividends are not mandatory and subject to the discretion of the company directors. If the preference dividends are omitted, nothing serious will happen to the company. Hence, to compensate for these shortcomings, the safety margins are higher for preference shares. 

To explain how the earnings coverage and current stock value ratio are computed, we use Hyflux as an example. The table below shows the income statement of Hyflux for the Financial Year (FY) 2012.

Table 3: Hyflux's Income Statement for Financial Year 2012

For FY2012, Hyflux reported a Profit before Tax of $77.0M. Adding back the finance cost of $28.5M and subtracting the share of profits from associates of $4.3M, there is $101.2M available to cover fixed charges. The fixed charges comprise the reported finance cost of $28.5M plus preference dividends of $24.1M, making a total of $52.5M. The earnings coverage is thus computed as $101.2M / $52.5M or 1.93.

On the stock value ratio, Hyflux has 825.2M of ordinary shares and 4.0M of preference shares. The last traded prices are $1.165 and $106.85 respectively. The market values work out to be $961.4M and $427.4M respectively. The stock value ratio is computed as $961.4M / $427.4M or 2.2.

How do the existing bonds and preference shares listed on SGX compare based on the 2 criteria mentioned above? The results based on the latest FY are shown below:

Company	Coupon	Earnings Coverage	Stock Value Ratio	Type
CMA	3.800%	4.01	13.6	Bond
Olam	6.750%	1.92	3.7	Bond
SIA	2.150%	5.37	39.3	Bond
DBS	4.700%	373.22	50.3	Pref
Genting	5.125%	7.33	34.9	Pref
Hyflux	6.000%	1.93	2.2	Pref
OCBC	4.200%	32.05	4.9	Pref
UE	7.500%	6.45	No Info	Pref

On earnings coverage, all the bonds and preference shares passed the criterion for Industrials with the exception of Olam and Hyflux. On stock value ratio, all the bonds and preference shares passed. Hence, all except Olam's bond and Hyflux's preference shares qualify as good fixed income investments.


See related blog posts:

• Is Benjamin Graham's Art of Bond Investment Outdated?
• Does FCL's 3.65% Bond Have Sufficient Margin of Safety?
• Does Aspial's 5.25% Bond Have Sufficient Margin of Safety?
• Does Perennial's 4.65% Bond Have Sufficient Margin of Safety?
• Does Oxley's 5% Bond Have Sufficient Margin of Safety?
• Does Aspial's 5.30% Bond Have Sufficient Margin of Safety?
• Do Hyflux's 6% Perps Have Sufficient Margin of Safety?
• Does SIA's 3.03% Bond Have Sufficient Margin of Safety?

Managing My Father's Money Has Become A Full Circle

After reading La Papillion's and Derek's blog posts on how they invested their parents' money, I also wish to share how I invested the money from my father. Because our circumstances are different, our portfolio allocations are also different.

The money did not come from my father, rather, the money came about because we sold a flat and bought a new one. Instead of using the sales proceeds from the old flat to pay for the new flat, we retained the sales proceeds as cash and took out a loan. Strictly speaking, it is my father's money, because he paid for the old flat. However, it could also be viewed as taking out a home equity loan which I am responsible for paying off (there is no change in the flat ownership). The money became a joint investment, and we set up a new joint bank, CDP and stockbroking account for the investment (on hindsight, this is an important step as it allows us to check how the account is doing).

The terms of the account are similar, it is "capital guaranteed" in the sense that I have to pay back the loan at the end of the loan tenure. It's hurdle rate is the loan interest rate of 2.6% (HDB concessionary loan interest rate). However, the investment horizon is much longer, at almost 30 years.

Because both my father and myself are share investors and because of the long time horizon, we invested the money in a portfolio of shares and cash. After reading the 2 gentlemen's blog posts and reviewing my own experience, I think our parents' investing experience and how the money is viewed have a very huge impact on how the money is eventually invested. On the first factor, my father is a share investor, so he is very comfortable with investing the money in the stock market. In contrast, my mother has bad experience with shares and unit trusts, so she is only comfortable with bank preference shares.

On the second factor, if the money is viewed as a stand-alone account with capital guarantee, then very likely I would have invested it mostly in bonds and preference shares. On the other hand, if the money is viewed as a loan for my own portfolio, the money would be invested in shares. There would be almost no change in the risk appetite. In my case, the money was viewed as a joint investment of both my father's and my money. So while the money was still invested in shares, it has a reduced risk appetite since my father's money is involved. Only good shares would be selected, and at the first sign of trouble, the respective shares would be sold out. This has resulted in smaller profits but also less losses compared to my own account.

Thinking back, managing my father's money has become a full circle. I guess a number of us would have the same experience as me. When I was in university, I would recommend to him which stocks to buy (I was not trained in stock analysis then), so in a sense, I was helping to manage his money. When the stocks made money, I would feel very proud of my recommendations. But when the stocks lost money, I would quietly go away hoping it would be forgotten in time. During the days of the Asian Financial Crisis, losses were not in the region of 30-40%, it was almost a complete wipe-out! But my father never blamed me for the losses.

Fast forward to today, we are now officially entrusted with our parents' money. I guess we have all grown to be more sensible and responsible in managing the money, understanding that the money is hard-earned and earmarked for our parents' retirement. Taking smaller risks and making smaller profits is more important than taking larger risks and making larger profits. 

The greatest satisfaction in managing my father's money is not in seeing how much money have made for the account, but in seeing the satisfaction on my father when he views how well the account is doing. This, to me, is priceless.


See related blog posts:

• Fishing for Future Generations
• Building A Lasting Portfolio for Future Generations

One Plus One Equals Two-and-a-Half

If 2 investments both return 5%, can a portfolio made up of these 2 investments return more than 5%? In theory, it should not be possible, but in reality, it is possible to wring out some extra return from these 2 investments. How is this possible? Through portfolio rebalancing.

Modern Portfolio Theory states that if 2 investments are not perfectly correlated, a portfolio made up of these 2 investments should result in lower risk. However, it does not mention that extra returns might be obtained from this portfolio. To prove that this is possible, we consider the returns and standard deviations of 5 indices over the last 25 years since 1988, as follows:

Index	Returns	St Dev
STI	5.0%	22.9%
DJIA	8.5%	14.4%
HSI	9.3%	25.7%
Nikkei	-1.6%	21.5%
FTSE	5.2%	14.6%

Table 1: Risks and Returns of 5 Component Indices

A portfolio of 2 of these indices is constructed, each with 50% weightage (e.g. 50% STI and 50% DJIA). A total of 10 such portfolios are thus constructed. The portfolios are rebalanced whenever the proportion of the indices deviate from the original weightage by 5%. The risks and returns of these 10 portfolios are assessed and compared to their component indices. Of the 10 portfolios, 2 of them actually exhibited higher return while 4 of them exhibited lower risk compared to both their component indices. Please see the tables below for the correlation among the indices, and the returns and risks of the 10 portfolios.

		STI	DJIA	HSI	Nikkei	FTSE
STI			40.3%	54.6%	21.3%	34.0%
DJIA		40.3%		38.2%	22.6%	59.7%
HSI		54.6%	38.2%		16.1%	34.9%
Nikkei		21.3%	22.6%	16.1%		21.0%
FTSE		34.0%	59.7%	34.9%	21.0%

Table 2: Correlation (R-square) Among 5 Indices

		STI	DJIA	HSI	Nikkei	FTSE
	Self	5.0%	8.5%	9.3%	-1.6%	5.2%
STI	5.0%		7.3%	7.6%	2.3%	5.5%
DJIA	8.5%			9.6%	3.9%	7.0%
HSI	9.3%				4.6%	7.7%
Nikkei	-1.6%					2.2%
FTSE	5.2%

Table 3: Return of All Portfolios Made Up of 2 Indices

		STI	DJIA	HSI	Nikkei	FTSE
	Self	22.9%	14.4%	25.7%	21.5%	14.6%
STI	22.9%		17.0%	22.7%	19.0%	16.8%
DJIA	14.4%			18.2%	15.5%	13.7%
HSI	25.7%				19.8%	18.2%
Nikkei	21.5%					15.5%
FTSE	14.6%

Table 4: Risk of All Portfolios Made Up of 2 Indices

From Table 3, a portfolio of 50% STI and 50% FTSE returned an average of 5.5%, higher than STI's 5.0% and FTSE's 5.2%. Similarly, a portfolio of 50% DJIA and 50% HSI returned an average of 9.6%, higher than DJIA's 8.5% and HSI's 9.3%.

From Table 4, a portfolio of 50% STI and 50% HSI has a standard deviation of 22.7%, lower than STI's 22.9% and HSI's 25.7%. Similar observations can be seen from the portfolios of STI-Nikkei, DJIA-FTSE and HSI-Nikkei.

In total, 6 out of 10 portfolios exhibit either higher return or lower risk compared to their component indices. However, none of these portfolios exhibit both higher return AND lower risk.

The reason why a portfolio can beat the returns of its component indices is because when a particular index is performing poorly, the index that is performing better is sold and the proceeds reinvested into the poorer-performing index through portfolio rebalancing. When the poorer-performing index rebounds, the portfolio achieves better return compared to either of its component indices.

Having said the above, the portfolios do not beat both component indices all the time. A plot of the returns of a $10,000 investment in the portfolio and its component indices indicate outperformance only during certain periods of time. See the charts below for the STI-FTSE and DJIA-HSI portfolios.

Figure 1: Performance of Portfolio of 50% STI and 50% FTSE

Figure 2: Performance of Portfolio of 50% DJIA and 50% HSI

Nevertheless, it cannot be denied that portfolio rebalancing provides benefits to investors either in terms of higher return or lower risk in majority of the cases. Portfolio rebalancing should be considered as part of any investor's arsenal of investment tools.


See related blog posts:

• Portfolio Rebalancing - A Fine Balancing Act
• Volatility is Your Friend
• Not All Market Indices Are Equal