Investments horizon

Typically long-term institutional investors include pension funds and life assurance companies. Their investment horizon is long-term, reflecting the nature of their liabilities. Often they will seek to match these liabilities by holding long-dated bonds. 

Textbook efficient frontiers using, say, one-year period returns suffer from a mismatch between the term of the observation period and the term of a typical investment horizon (for which there may well be a linker of appropriate term). For long-term investors, it is not a particularly good way to examine inflation-linked bonds. 

In order to answer the question what share should be taken up by corporate bonds in a portfolio, ex post simulations were run. The Markowitz approach of portfolio optimization is based on using expected returns. Since the question of determining the optimal fixed income portfolio is to be answered against the background of historical data, the return and variance/covariance estimators are replaced by their historical return means and variances/covariances respectively. These historical data are computed congruently to the relevant investment horizon. For a 3-year investment horizon, the return means and variances/covariances of assets are computed on the basis of 36 monthly returns. The same is, in analogy, done for a 5-year investment horizon on the basis of 60 monthly returns. Investment horizons of three, five, and 10 years are analyzed here. For the investment horizon of, for example, five years, the monthly data in the time window from February 1980 to January 1985 are used. 

After computing the optimal weights, the time window was shifted forward by one month and the calculations repeated with the data from March 1980 to February 1985 (so called rolling approach ). This allows us to check the implications of various investment horizons of investors on the allocation of funds. 

The database consists of 275 monthly data sets. For a 5-year investment horizon, 60 data sets are required for every rolling computation of the optimal portfolio. This means that 215 (= 275 - 60) rolling calculations must be run for the 5-year investment horizon (3 year 239, 10 year 155). Averaging the weights over all 215 (239, 155) rolling calculations gives an indication of the optimal allocation of funds in a bond portfolio for a 5-year horizon (3-year, 10-year horizon). 

Exhibit 27.4 shows the average portfolio weights (in percent) for different investment horizons and risk attitudes, divided into the rating segments AA, A, BBB, and T (columns 2 to 5) or the term structure 1-3 year, 3-7 year, 7-10 year, and 10Y+ (columns 6 to 9). The sum of the weights in columns 2 to 5 is 100%, as well as the sum of columns 6 to 9. Rows 3 and 4 contain the optimal weights for the 3-year horizon, rows 6 and 7 those of the five year, and rows 9 and 10 those of the 10-year horizon. 

The risk averse investor with an investment horizon of three years (row 3) allocates his capital according to the weights in 8% corporate bonds with AA rating, 15% in A, 70% in BBB, and 8% in Treasury bonds (columns 2 to 5). His optimal term structure consists of 52% bonds with a 1-3Y maturity, 6% with 3-7 year, 5% with a 7-10 year, and 37% with a 10 year+ maturity (row 3, columns 6 to 9). 

Focusing on the term structure of the optimal portfolios, the portion of longer maturities increases when risk aversion is reduced. The aggressive investor with a 10-year horizon, for example, invests the whole capital in 10-year+ maturities, the averse one only 78% (rows 9 and 10, column 9). According to investment horizon, the 3-year risk averse portfolios consist of 52% short-term maturities in the 1-3-year area (row 3, column 6). The aggressive style, on the other hand, allocates only 26% to this maturity bucket (row 4, column 6). 

Exhibit 27.5 shows the average weights of the optimal portfolios in detail depending on both rating segment and term structure for the three investment horizons. 

EXHIBIT 27.5 Average Weights of the Optimal Portfolios in Detail Depending on Rating Segment and Term Structure for the Three Investment Horizons (%)... 

The maximum CR of the aggressive investor with a 3-year horizon, for example, is 21.8% (row 3, column 4). A value of 19.4% in row 6, column 4 (quantile 95% for the aggressive investor) means that only 5% of the optimized portfolios realized a value higher than 19.4% in the 239 rolling calculations of the 3-year horizon. For the 10-year horizon and a risk averse attitude, the minimum CR was 7.2% per annum (row 4, column 7). The average CR for this investment horizon for the risk averse investor was 11.5% (row 9, column 7). 

For an investment horizon of at least three years it pays on average to include risk in the form of corporates in a bond portfolio the optimized portfolios contained 58% to 79% corporates of the BBB segment. The A category was represented with portions between 0% and 15%, the AA corporates between 0 and 8%. Treasury bonds were weighted between 8% and 35%. 

The term structure changed with investment horizon and varying risk attitude the higher risk aversion, the greater the portion of corporates (due to their superior risk/return characteristics versus Treasuries in... 

To assess the value of a mortgage-backed bond over a given investment horizon, it is necessary to measure the return generated during the holding period from the bond s cash flows. This is done using the total return framework. 

B. Hall, "Corporate restructuring and investment horizons in the United States, 1976-1987," Business history review, 68 (1994), 110-143. 

The simple interest rate that was calculated in the previous section assumed an addon type of interest. The distinction between add-on interest and compound interest is not really important except in the direct comparison of securities with different maturities. In other words, an investor must be concerned with the actual investment horizon. 

If the investment horizon is 360 days and if each of these securities could be rolled over at their stated discount rate, the effective rates of return would be... 

Hall, Bronwyn (1994) Corporate Restructuring and Investment Horizon in the United States, 1976-1987, Business History Review, Spring 1994, p. 110-43. 

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