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.
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| 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.
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| 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.
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| 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.
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| 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.
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