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Weekly Updates2. METHODOLOGY AND DATA
The benefits of managers diversification are measured in real estate market of Ikoyi and Victoria Island areas of Lagos Metropolis, Nigeria. This is done with the belief that if benefits of managers diversification can be measured in these relatively homogenous markets, then they are likely to be found elsewhere. The sample is annual transaction data for residential properties obtained from three major property investment and development companies in Nigeria for five-year period from 1997 through 2001. These companies are WEMABOD Estate Limited, UACN Property Development Company and Stallion Property Development Company. This period, in the Nigerian property markets, can be divided into two sub-periods. These are (i) 1997 to 1999, which is characterised by expansion and positive growth in most of the Nigerian markets and (ii) 2000 to 2001, which reflects the beginning of contraction phase following the positive growth in rent, positive but slow growth in demand and the greater than demand increasing supply. The scope of the study was restricted to a consideration of diversification options within residential property sector only. Also, the properties included in the sample were those located within Ikoyi and Victoria Island property markets in Nigeria. This restriction in scope is done in a concerted effort to control or remove the gains that may be obtained from investing in different property sectors and locations. This thus limits our consideration of the benefits of diversification to different manager's skills.
The managers of the three companies sampled were asked to give data on performance levels of residential properties, located in the study areas in their respective portfolios in aggregated form. In other words, the study adopted aggregated approach on properties' performance with the performance of each property type sampled reflecting the average performance level of all the individual property type contained in each manager's portfolio. This reduction in scope is necessary because property companies in Nigeria prefer giving out needed data on properties' performance levels in aggregated form rather than on an individual basis for confidential reason. Although, this methodology, according to Geltner (1991), tends to understate the volatility of the real estate market especially because the property values are appraisal based, the author opined that the bias becomes a systematic error since it has a similar impact on all the properties included in the analysis.
Annual internal rate of returns on each of the property type and in each of the three managers' portfolios were estimated as:
[C.sub.0] = [R.sub.1] - [P.sub.1]/[(1 + [r.sub.m]).sup.1] + [R.sub.2] - [P.sub.2]/[(1 + [r.sub.m]).sup.2] + ... [R.sub.t] - [P.sub.t]/[(1 + [r.sub.m]).sup.t] ...... + [C.sub.n] + ([R.sub.n] - [P.sub.n])/[(1 + [r.sub.m]).sup.n], (1)
where: [r.sup.m] is the internal rate of return (IRR); [R.sub.t] is the income received in period t, t = 1, 2, 3, ... n; [P.sub.t] is the net purchase/outlays in period t, t = 1, 2, 3, ... n; [C.sub.n] is the value of the property at the end of period n (measurement period); [C.sub.0] is the initial cost of investment or capital value of the asset at the beginning of the measurement period; n is the number of time-period (measurement period).
The result is a return series for each of the managers named A, B, C (see Table 1) from which optimal (efficient) portfolios were constructed using constant correlation model. The calculations were based on the assumption that investments are held long. The use of this method is preferred to the traditional mean variance analysis because of its reduced mathematical complexities. Thus, it allows a portfolio manager to quickly and easily determine the optimum portfolio without much mathematics as in Markowitz's mean variance model. Besides, it is the expectation that the Nigerian investors will support a less complex analysis since, like other investors, they are loath to invest on the basis of allocation system that they do not understand. Also, it is the authors' belief that mean variance analysis is best suited for a developed real estate market where there is evidence of time-series data and investments can be held short. Where property market is yet to be fully integrated into the capital market operations and most investments are held long, such method as mean variance analysis can produce misleading results. In addition, the use of constant correlation model also allowed us to single out just six portfolios for testing against the naive portfolios and thus we do not have to test every single efficient portfolio which, off-course, is infinite in number. The six portfolios tested were based on +1, +0.5, +0.1, -0.1, -0.5 and -1 correlation coefficients between each pair of asset.
The procedure for this model as described by Elton and Gruber (1981) involved, basically, three steps. First, assets are ranked by their excess return to standard deviation as:
([R.sub.i] - [R.sub.f])/[[delta].sub.i] (2)
Second, a cut-off rate [C.sup.*] which determines how many assets are selected in the optimal portfolio, will be fixed by first calculating the cut-off rate [C.sub.i] for each assets as thus:
[C.sub.i] = [rho]/(1 - [rho] - i[rho]) x [i.summation over (j=1)] ([[bar.R].sub.i] - [R.sub.f])/[[delta].sub.i], (3)
where: [rho] = the correlation coefficient--assumed constant for all securities; [C.sub.i] = calculated cutoff rate for asset i.
The cut-off rate ([C.sup.*]) is then fixed such that all assets/properties with higher ratios of ([R.sub.i] - [R.sub.f])/[[delta].sub.i] than their [C.sub.i] will be included in the optimal portfolio and all assets with lower ratios excluded. Third, the optimal amount, which must be invested in each asset, is calculated as:
[X.sup.0.sub.i] = [n.summation over (i=1)] [Z.sub.i]/[Z.sub.i], (4)
where: [Z.sub.i] = 1/(1 - [rho])[delta] x {([R.sub.i] - [R.sub.f])/[delta] - [C.sup.*]}. (5)
Following from the procedures described above, optimal portfolios are constructed and their efficiency compared with the various naive portfolios developed so as to determine the superiority or otherwise of the naive diversification schemes. These naive diversification portfolios are based on:
1. Equal allocation between managers (1 portfolio).
2. All investment in one manager (3 portfolios).
3. Equal allocation between managers with the allocation to each manager spread evenly among the property types in the manager's portfolio (1 portfolio).
4. Equal allocation between managers with the allocation to each manager invested in one property at a time (13 portfolios).
In all, 18 different naive diversification portfolios were considered and their mean/standard deviation ratio as well as effectiveness of diversification compared with the efficient portfolios.
The mean standard deviation criterion holds that portfolio A from strategy X is better than (or dominate) portfolio B from strategy Y if M/[delta] ([P.sub.a]) > M/[delta] ([P.sub.b]). A higher ratio is associated with higher portfolio efficiency. In addition, portfolio efficiencies are viewed in terms of their effectiveness of diversification measure. This expresses the percentage reduction in risk achieved by holding a variety of different assets, which is borne out of the fact that in modern portfolio theory, the risk of a portfolio, as measured by the standard deviation of returns, is less than the weighted average risk of the individual constituent assets. Thus, by comparing the risk of portfolio return (R) with the weighted average risk of individual assets (W), it should be possible to produce a measure of the effectiveness of diversification (Ajayi, 1998 quoting Lumby, 1984). It is measured as:
Effectiveness of Diversification = (W - R)/W. (6)
The higher the ratio, the higher the efficiency of diversification.
3. RESULTS
In the study, 18 different naive portfolios were constructed for use as benchmark. They are based on:
(1) Diversification by manager (wherein property purchase is not given consideration) and where investments were either solely in one manager (3 portfolios) or in equal allocations to each of the three managers (1 portfolio).
(2) Diversification of managers and property types wherein property purchases are considered. Here, we considered (a) equal allocation to managers with the allocation assumed to spread evenly among the property types in each manager's portfolios (1 portfolio), and (b) equal allocation to managers with the allocation to each manager invested in one property type at a time (13 portfolios). Table 2 presents the returns (and standard deviations) of these benchmark portfolios. The results show that they range from 15.79 (0.274) to 21.96 (1.154) for managers' diversification only and 15.81 (0.253) to 23.65 (1.258) for managers and property types diversification. Returns and risks tended to be higher for managers and property types diversification than for manager diversification only. Also, the diversification strategies of equal allocation across managers and property types with the allocation invested in one property type in each manager's portfolio produced a better (dominant) portfolio with the strategy of diversifying equally across managers and property types ranking second. The diversification strategy of equal allocation to each manager's portfolio ranked third in efficiency level, in terms of mean/standard deviation ratio.
3.1. Residential Diversification by Manager (Efficient Portfolios)
The results of diversification by manager are shown in Table 3. The results include the standard deviation, mean returns, weights mean/standard deviation ratio and effectiveness of diversification of the six efficient portfolios constructed. Among these portfolios, the portfolio that is based on correlation coefficient of 0.1 produced dominant results in terms of mean/standard deviation ratio and effectiveness of diversification. Also, the range of results is less than those realised for naive diversification strategies. Range of results is 4.07 vs 6.17 for efficient and naive portfolios respectively. It is also noted that the dominant portfolio (in terms of mean/standard deviation ratio) outperformed the naive diversification based on this strategy but has a lower effectiveness of diversification of 0.6206 as against the naive diversification effectiveness of 0.6684. One other thing noted in these results is that, on the average, portfolio efficiency tends to increase with the reduction in the correlation coefficient.
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