Analysis of the assets used to construct the diversified portfolios

In this section a comparative analysis is performed on the assets identified in the previous section. The purpose is to indicate the performances of the individual assets and their risk characteristics, but also to evaluate the co-movements of the assets.

6.2.3.1 Performance analysis

Figure 6.1 represents the weekly movements of the ALBI index over the 730-week observation period.

Figure 6.1

Weekly All Bond Index (ALBI) movements 1990 - 2003

0 50 100 150 200

1989/12/31 1990/12/31 1991/12/31 1992/12/31 1993/12/31 1994/12/31 1995/12/31 1996/12/31 1997/12/31 1998/12/31 1999/12/31 2000/12/31 2001/12/31 2002/12/31

Date

Index Level

Source: Inet

Figure 6.1 indicates that the index has increased over the observation period.

Figure 6.2 represents the weekly movements of the All Share Index (ALSI) over the same holding period.

Figure 6.2

Weekly All Share Index (ALSI) movements 1990 - 2003

0 2000 4000 6000 8000 10000 12000 14000

1989/12/31 1990/12/31 1991/12/31 1992/12/31 1993/12/31 1994/12/31 1995/12/31 1996/12/31 1997/12/31 1998/12/31 1999/12/31 2000/12/31 2001/12/31 2002/12/31

Date

Index Level

Again the index increased over the holding period.

Figure 6.3 represents the weekly movements of the 90-day BA-rate over the holding period (1990 – 2003).

Figure 6.3

Weekly 90-Day BA yield-rate (BA) movements 1990 - 2003

Source: Inet

In contrast to the other assets the yield on the 90-BA has declined over the holding period.

Lastly figure 6.4 indicates the price movement of the Kruger Rand asset over the same holding period.

Figure 6.4

Weekly price movements of the Kruger Rand

0 500 1000 1500 2000 2500 3000 3500 4000

1989/12/31 1990/12/31 1991/12/31 1992/12/31 1993/12/31 1994/12/31 1995/12/31 1996/12/31 1997/12/31 1998/12/31 1999/12/31 2000/12/31 2001/12/31 2002/12/31

Date

Price Movement

Source: Inet

Figure 6.4 indicates that the Kruger Rand’s price increased over the observation period. The steepness of the trend line in figure 6.4 would lead one to suspect that the price increase experienced by the asset was greater than that of all the other assets considered.

Direct comparisons between the returns on these assets are not possible from the charts cited above. Only general inferences, such as the ones made with regards to a general increase or decrease in the price of the asset or index level are possible. In order to directly compare the performances of the assets over the holding period, asset returns had to be standardized. This was done by calculating the holding period yield (HPY) for each asset. Note that in this case a week represented an individual holding period.

The following equation represents the calculation of HPY:

−1

= HPR

HPY [6.1]

Where: HPR represents the holding period return (calculated by dividing the end value of the asset by its initial value, for a specific holding period).

Figure 6.5

Weekly HPY for the ALBI (1990 – 2003)

Source: Inet

Figure 6.5 represents the holding period yields for the ALBI (debt investment) during the period Jan 1990 to Dec 2003. Of this figure it may be said that most of the observations lie in the band between –2.00% and +2.00%, however, there are some outliers as indicated by points A and B on the figure.

Only when it is compared to similar figures for the equity asset and the cash component of the diversified portfolio can the debt instrument be properly

Figure 6.6

Weekly HPY for the ALSI (1990 – 2003)

Source: Inet

Figure 6.7

Weekly HPY for the BA (1990 – 2003)

Source: Inet

Figure 6.6 indicates that even though there were some outliers (as indicated by A and B), most of the observations (HPY) for the ALSI were concentrated

figure 6.7) the returns are represented on an annualised basis and as such the cash investment never produced a negative return.

Figure 6.8

Weekly HPY for the Kruger Rand (1990 – 2003)

Source: Inet

Figure 6.8 indicates the weekly HPY for the Kruger Rand asset during the period ranging from 1990 to 2003. The chart indicates that on average the Kruger Rands provided investors with a weekly return ranging between –5%

and +5%.

In order to directly compare the returns on the various investments, it is essential to annualise the return figures. These figures should be annualised using equation 6.2:

[

]

HPY

Annual = π ¹ⁿ − [6.2]

Applying this equation to the returns of the different assets produced the

Table 6.1

Table of comparative performance measures

Asset Simple Average HPY Annualized HPY

Debt 0.06% 2.98%

Equity 0.22% 10.09%

Cash 13.93% 13.93%

Kruger Rands 0.16% 7.40%

Source: Inet

Table 6.1 indicates that the debt investment proved to be the worst performer of all the assets considered, in terms of return. On the other hand cash investment seems to have outperformed all the other assets based solely on return.

From the discussion on portfolio theory it was apparent that securities and portfolios should not be assessed based solely on returns, but that the risk of each asset should also be considered. The following section will briefly consider the relevant risk measures for each of the assets.

6.2.3.2 Risk analysis

The initial chapters of this study identified the measures of variance and standard deviation as the most widely used and recognized measures of investment risks.

From that discussion it transpired that the higher the level of standard deviation, the higher the risk associated with the asset. Also the discussion on the capital market theory indicated that investors would expect a direct relationship between risk and return. Thus if risk increases so too should return.

This section of the study uses probability distributions of asset returns to illustrate the degree of standard deviation for each of the assets. Figure 6.9 illustrates the probability distributions for each of the assets mentioned in the previous section, starting with debt instruments, moving to equity investments cash and ending with the Kruger Rand.

Figure 6.9

Probability distributions of assets

Source: Inet

Figure 6.9 (note that each of the figures is based on the same scale) indicates that the cash investment proved to be the most risky asset of the assets being analysed. This conclusion may be made by considering the extent to which the returns of the asset tends to deviate from the mean. The wider the dispersion around the mean the higher the risk associated with the asset. The kurtosis (level of peakedness) of the distribution of the debt instrument indicates that this asset is represented by a leptokurtic distribution, which indicates that this asset tends to have a high concentration of returns situated around the mean. When compared to the more platykurtic distributions of the

investments. When considering these risk measures in conjunction with the return analysis it may be said that the results are in line with the belief that return should increase as risk increases.

Table 6.2 lists the percentage annual volatility for each of the assets. This measure is an annualised standard deviation figure for each of the investments and as such these figures were calculated by applying the following formulae:

In order to derive the percentage annual volatility the calculated standard deviation is annualised.

Table 6.2

Percentage Annual Volatility of assets Percentage

Annual Volatility

Debt 8.86%

Equity 19.48%

Cash 22.77%

Kruger Rands 15.50%

Source: Inet

Table 6.2 confirms the results indicated by the probability distribution curves cited in figure 6.9. In addition to this it allows investors to rank the assets in order of riskiness. For this section cash investments represent the most risky of the assets, whilst debt instruments represent the lowest risk.