Risk-averse investors

One might expect securitization to be of greatest benefit to riskier companies. This expectation, however, is only partly true. As a company moves toward the extremes of financial instability and towards the brink of bankruptcy, securitization is less of a benefit. At this point, the SPV has a higher than normal risk of being challenged by the originator s trustee in bankruptcy, and risk-averse investors tend to avoid these transactions. 

The existence of these uncertainties or risks may cause the business or government executive to incorrectly estimate expected costs and the likelihood of technical success. Given the inability to correctly or objectively assess risk-uncertainty and hence expected costs, the risk-averse investor might be expected to undertake less R D than otherwise for a fixed level of benefits likely to flow from a successful innovation. Thus, in the absence of government Investment, there may be under-investment in areas of high technological risk—particularly where the costs of R D are high and the resources of private companies are limited. 

Risk attitudes depend on personality, life experience, wealth, and other socioeconomic factors. By default, extremely risk-averse investors are not interested in buUding wealth via asset accumulation, because they are unwiUing to tolerate the risk necessary to obtain high returns. The opposite is true for adventurous souls ready to gamble for large payoffs. In this regard, old-money investors... 

When optimizing the return of the portfolio, risk has to be taken into account. Within a shortfall risk approach the portfolio is optimal that falls short of a user specified minimum return (e.g., r, in = 0%) with a given shortfall probability p (e.g., 10%). A very risk averse investor requires a higher minimum return and a lower shortfall probability than a less risk averse one. Exhibit 27.2 displays this graphically in the risk/ return diagram. 

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). 

According to Exhibit 27.5, for example, the risk averse investor with a 3-year horizon allocates 4% of his capital to AAl-3-year corporates (row 3, column 2). The 3-7-year segment of this rating category is represented with 2% (row 3, column 3), whereas AA7-10-year is not included (row 3, column 4). 

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). 

A good rule of thumb is that if you are a very risk-averse investor, you should plan to invest money that you won t need. Then, invest this money in bonds that fit your risk and financial profile and hold the bonds until maturity. 

Once the efficient frontier is established, the issue of investor risk preferences must be addressed. Individuals exhibit markedly different attitudes towards risk. Some are extremely risk averse, tolerating nothing but near certainty in life. Others relish risk taking. Most are somewhere between these two extremes. 

How does one ascertain risk tolerance to guarantee a relevant portfolio is matched to the investor s needs There are a number of ways. One is to estimate the risk-aversion parameter based on the investor s response to a battery of questions designed to trace out their return preferences with different payoff probabilities. 

The additional compensation or spread over the benchmark yield that investors will require reflects the additional risks the investor faces by acquiring a security that is not issued by a sovereign government. These yields spreads (discussed later in the chapter) will depend not only on the risks an individual issue is exposed to but also on the level of benchmark yields, the market s risk aversion, the business cycle, and so on. 

This may all seem rather convoluted, so a simple example might suffice to make the point clear. Let us assume that the average bond investor expects future long-term inflation to be 2.5%, and that the average investor is inflation risk averse, so be prepared to pay a 0.25% risk premium. On this basis alone, we would expect observed break-even inflation to be 2.75%. Now let us say that the govermnent also has inflationary expectations of 2.5%, but it prefers real liabilities to nominal liabilities, and places a 0.25% yield value on that preference. It will prefer to sell inflation-linked bonds rather than nominal bonds until break-even inflation falls to 2.25%. 

The swap yield curve is correlated with the Treasury yield curves, but this correlation has decreased from 2001 to 2002. This may be explained by the increase in the investors risk aversion as continuing poor performance of equity markets in 2002 has triggered a search for liquidity and quality. The correlation with the Treasury yield curves is high for the first factor (see Exhibit 24.4), but weak for the second and third factors (see Exhibits 24.5 and 24.6). 

QS is the shortfall line and depicts expected return of portfolios along the line QZ that are equal or higher than the return of QS in (1 - p)% of all cases. Portfolio returns fall short of QS in p% of all cases. Portfolio P (corresponding with point P" on the shortfall line QS) reaches a return of tjnin in (1 - p)% of all cases and thereby complies with the investor s risk aversion. The optimal portfolio P maximizes return taking the investor s risk aversion into account. The following equation formalizes the investor s risk aversion. It is assumed that returns follow a normal distribution. 

Utilizing the shortfall risk framework an investor s risk aversion can be described more clearly than for example, with a utility function. A common utility function is U = L X fp - Op (William F. Sharpe, A Simplified Model for Portfolio Analysis, Management Science 9 (1963), pp. 277-293). Here determination of the parameter X, which measures the investor s risk aversion, is a problem. 

Equation (27.2) describes a line with slope k starting from point Q in the risk/return diagram (Exhibit 27.2)7 Maximization of the expected portfolio return in equation (27.1) in compliance with equation (27.2) exactly describes the investor s risk aversion. Additionally, the following collateral conditions are set ... 

Surprisingly, the share of Treasury bonds increases with lower risk aversion (column 5). Conversely, corporates make up a higher portion of the portfolio the greater risk aversion is. This is due to the inferior risk/return characteristics of government bonds relative to corporates (Exhibit 27.1). For a 5-year horizon, for example, the risk averse portfolios consist of 71% BBB corporates, whereas this share declines to 64% for the aggressive investor (rows 6 and 7, column 4). 

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). 

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