Description
The data for this paper has been chosen to imitate the investment habits of a risk adverse investment manager. This includes, as mentioned in the introductory chapter, investing in both stock and bonds and largely diversified investing both geographically and sector based. To avoid a big section on the analysis of stock and bond picking, the assets have been limited to stock indices and long-term government bonds indices including a High-Yield bond index from the US, all chosen after discussions with the supervisor of this paper. The geographical diversification leaves the portfolio with assets from North America, Europe and the Pacific represented by Asia/Australia. The time series for the assets goes back 18 years which should be enough to make a usable statistical analysis that includes both times of recession and times of financial growth, and in that sense will be robust regardless of the times.
For the stock part of the portfolio indices from the company Morgan Stanley Capital International (MSCI) are being used, a company dedicated to “bring more transparency to the financial markets” (MSCI, 2019). They are known to create indices to almost all markets globally and their indices are “ … designed to measure the performance of the large and mid cap segments of the markets… The indices cover approximately 85% of the free adjusted market capitalization in the respective market.” Free float-adjusted market capitalization is a best practice method of calculating the market
capitalization of companies and only take the publicly available shares into account. This gives a more realistic and proportional view for companies being traded in a specific market. All three MSCI indices being used in this paper are Gross Return Closing reads.
Following leaves some background information and explanation of the time series used in the paper.
MSCI US
This index consists of 637 constituents of the US market, with the largest contributors being Microsoft, Apple, Amazon and Facebook. These 4 corporations make up approx.
10% of the total index. Following shows the top constituents, the sector weights, and the yearly result in % the last 14 years:
It is noticeable that IT, Health Care and Financials are the top 3 sectors in the index, and interesting is also the large difference in performance over the years.
MSCI EU
This index is made up from companies from 15 countries in Europe. Below is the
different weights regarding country, the sector weights, and the yearly performance the last 14 years. Not surprisingly the index relies heavily on the UK, Switzerland, France and Germany. As with the US Financials and Health Care are high among the sectors.
MSCI Asia
The MSCI index from ASIA consists of companies from 12 countries in Asia. Japan and China make up by far the most geographically, and IT companies and Financials are two of the largest sectors. Following is the Constituents, the country weights, the sector weights and the Yearly Returns from the last 14 years. As with the US and EU index, it has been very volatile over the years.
Following is the developments for the three MSCI indices. It is interesting to note how similar they are to each other over time. Later in the chapter the correlations will be analyzed, but it is clear that economic downturns for one MSCI index generally will see the other two experience a similar downturn.
Government Bonds
The 7 country bonds indices in this paper are all Thomson Reuter 10 Year Government Benchmark Indices. These indices are an estimation of the price of a 10-year bond, taken from a basket of bonds with maturities around 10 years. This is done because not all countries have bond with maturity in 10 years available on the market to use for pricing.
In the following is the developments in the Government index for the US10Y, the
German 10Y and for the Japan 10Y. It is interesting to see how the US seems more volatile than the other two, but most interesting is to see how constant the returns and volatilities are for bonds compared to the three MSCI indices above.
High Yield
The last bond index in the paper is the Merrill Lynch US High Yield Master II Index. This is a broadly used benchmark index that includes a series of High Yield Corporate bonds and as opposed to other high yield indices, it takes into account the whole high yield market where others tend to leave out lower rated securities. The development for the High Yield index follow below, and it is interesting to see it seems like a mix between and MSCI index and a Government bond.
After the 11 time series where attained, a data cleansing effort was put forth. The time series were checked for outliers and typing mistakes by examination of plots of the values of the different series against time. After this the returns of each series was plotted against time, and also here where examined for extreme values, that would suggest mistakes. At both examinations no observations were deemed to be significantly unrealistic and therefore no values were corrected. After the search for outliers the data was compiled into one dataset including all data points from each date reported in either asset series. Because of different closing and holidays geographically and because of different start/end dates for the different series, this resulted in large number of “NA”
(Not Available) data points for many dates. In order to make the dataset more usable in statistical analysis, all dates without a data reading from all 11 assets were taken out of the data set. Of course this will lead to misleading returns from one date to another for the series where one or several data points are taken out in between, but it was deemed that as long as the all the assets had the same time frame between the dates they would still be comparable to one another. As all time series as noted in the local currency it was also necessary to adjust for the currency exchange rate. According to covered interest parity this is best done with forward contracts on the different currencies, but it was deemed that the difference in the 1M LIBOR for the different countries divided by 100*252 would be a close enough approximation to a daily currency swap. As the paper simulates a company under the Solvency II regulation all returns are denominated in Euro after the adjustment for currency exchange.
Finally because of the intent to compare with the regulations of Solvency II the series of Solvency Capital Requiremnt (SCR) was found on the EIOPA website. This is a cross the board estimate, of the 99,5% worst-case scenario over a one year period for investing in risky assets as stock. This time series was also put through a data cleaning process, as it
was examined visually for outliers. Following this process it was deemed unlikely to include extreme values and thus was not changed. As with the other time series, it was adjusted to have the same length in order to be more comparable.
Analysis
A brief look at the development of one stock index, one bond index and the high-yield index shows that they react differently when it comes to economic shocks in the economy. In red is the recession in 2008-2009.
Where both the US stock index and the High-Yield index reacts negatively to the
financial troubles of these times, the US bond index increased. This is a natural reaction however as investors in times of recession tend to move into more secure assets as government bonds, and therefore the price of such assets are driven up in these times. It is also worth noting the difference in volatility in the three assets, as the stock index
clearly has more, and more sporadic, movement as its two bond counterparts. Since bond returns are more stable, so is the pricing and especially government bonds that are among the trustworthiest assets will therefore have considerably less movement
because of this security in the asset. In the appendix of the digitally uploaded version of this thesis a copy of all time series are attached to show how they all react to the
different financial up and down turns. To analyze the developments further, the returns of each asset was calculated for each of all the time series. The return series of an asset will give an indication if there is any seasonal or time-dependent variance for the asset.
Following is the return series for the same three assets used to analyze the price
development. The return series is calculated as the log difference from one data point to the next.
The red lines on the plot indicate times with particularly high volatility. These types of clusters are sign of the presence of heteroskedasticity in the time series and a cause for warning when it comes to modeling the volatility without taking this into account.
Heteroskedasticity means that the volatilities are not homogeneous throughout the data set. Another reason for heteroskedasticity could be seasonal changes in the volatility.
This would require the clusters of spiked returns to be with regular intervals. However, looking at the three time series, it is clear that there are no seasonal spikes in variance over time. Noticeable though, is the lack stability in the random changes in the three time series, as earlier mentioned a sign of heteroskedasticity. These periods with considerably higher variance, and periods with low variance suggest that different observations have different volatility. A Ljung-Box test on the squared residuals over time will give an estimate of the likelihood of the presence of heteroskedasticity, this test along with others, will be carried out in the chapter dealing with the statistical analysis.
After the process of data cleaning, merging and individual examination of the different time series, they were examined against one another. First a full period static correlation matrix was calculated to see how the different assets reacted relatively over time.
Following is the correlation table.
US EU ASIA US10Y CA10Y JP10Y AU10Y UK10Y GE10Y FR10Y HY US 1.00 0.58 0.17 -0.37 -0.36 -0.04 -0.09 -0.25 -0.27 -0.20 0.27 EU 0.58 1.00 0.36 -0.36 -0.31 -0.09 -0.20 -0.40 -0.41 -0.30 0.47 ASIA 0.17 0.36 1.00 -0.06 -0.04 -0.25 -0.30 -0.10 -0.11 -0.04 0.44 US10Y -0.37 -0.36 -0.06 1.00 0.80 0.10 0.16 0.56 0.58 0.49 -0.10 CA10Y -0.36 -0.31 -0.04 0.80 1.00 0.10 0.16 0.54 0.54 0.48 -0.06 JP10Y -0.04 -0.09 -0.25 0.10 0.10 1.00 0.27 0.16 0.17 0.14 -0.06 AU10Y -0.09 -0.20 -0.30 0.16 0.16 0.27 1.00 0.28 0.31 0.24 -0.15 UK10Y -0.25 -0.40 -0.10 0.56 0.54 0.16 0.28 1.00 0.80 0.71 -0.15 GE10Y -0.27 -0.41 -0.11 0.58 0.54 0.17 0.31 0.80 1.00 0.84 -0.15 FR10Y -0.20 -0.30 -0.04 0.49 0.48 0.14 0.24 0.71 0.84 1.00 -0.07 HY 0.27 0.47 0.44 -0.10 -0.06 -0.06 -0.15 -0.15 -0.15 -0.07 1.00
As stock and bond are to relatively opposite assets (risky/risk adverse), it is expected that they do not correlate very well. This is confirmed as all three stock indices are negatively correlated with all the bond indices. They are particularly negatively
correlated against their own geographical counterparts, which will give stability in the portfolio with each asset having a counterpart to balance it out. The High yield is positively correlated with the stocks and slightly negatively correlated with the bonds, and will have a dampening effect if the bonds go down. It is expected that asset classes correlate higher internally, and especially when they are from the same geographical area. Therefore it is no surprise that the North American bonds and the European bonds correlate strongly respectively, but it is interesting to note the limited correlation
between the Asian bonds and the Australian bonds. As the intentions of the asset choices were to make open for the option to make a diversified portfolio, the correlation matrix supports exactly that. It can be noted that some assets like the US and CAN bond indices correlate to a level where it would simplify to just use the one, but although having both will make statistical inferences more complex, it also serves as an insurance in case something specific happens in either the American or Canadian economy.
Now that the data has been introduced, the next chapter will perform statistical analysis on this data in order to answer the question set forth in the problem formulation.