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«Oscar Stolper (University of Giessen) Andreas Walter (University of Giessen) Discussion Paper Series 1: Economic Studies No 23/2011 Discussion Papers ...»

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by relaxing the assumption that investors are equally ambiguous about all assets. This modification is particularly suitable for asset allocation decisions, since an individual’s ambiguity aversion is extra high in comparative situations where different chances are compared against each other instead of being evaluated separately. They find that, when admitting investors to exhibit different degrees of uncertainty across assets, the portfolio selection deviates from the Markowitz theory in two important ways. The first difference concerns the portfolio composition. The optimal portfolio is now composed of a mix of familiar and unfamiliar assets. Put differently, incorporating familiarity as a selection dimension implies that the resulting portfolio is exposed to idiosyncratic risk. The second deviation concerns the portfolio’s sensitivity to risk. The familiarity bias triggers a rebalancing of the optimal portfolio in response to changing asset-return correlations. In fact, Boyle et al. (2011) find that the fraction of familiar assets increases in times of a financial crisis―an effect which they dub flight-to-familiarity.

The intuition for this result is that unfamiliar assets become less useful for diversification purposes as correlations between assets increase. An ambiguity-averse investor will therefore hold relatively less of the unfamiliar assets. If geographic proximity is a valid proxy for familiarity, we would thus expect investors (i) to hold locally biased equity portfolios (which we show in section 2 of this paper) and (ii) to shift their portfolio towards local stocks in times of stock market downturn, resulting in an increased local bias during those periods. This second implication is tested in the following.

5.2 Methodology

To test for a potential familiarity-driven investment behavior, we use expected stock return volatility as a measure of investor uncertainty in order to gauge the negative relationship between asset price standard deviation and returns.33 To this end, we take the VDAX New index which captures implied volatility of the DAX30 index at a one-month horizon and may be regarded as the German equivalent to the CBOE’s market volatility index VIX based on the S&P 500. We calculate quarterly means of the VDAX New and compare them to the corresponding local bias levels at the end of each quarter.

Before turning to the test, we are interested in the extent to which overall quarterly changes in local bias levels actually reflect active portfolio rebalancing decisions. Note that individual investors’ exposure to local assets may change in two ways. Obviously, they can play an acSee Schwert (1990), among others, for an examination of the relationship between asset price volatility and returns.

tive part by trading and thereby altering the proportion of local equity in their portfolio. On the other hand, however, they may allow price changes to naturally shift the relative weight of nearby―as opposed to remote―companies. To distinguish these effects, we dissect the quarterly changes in local bias into a trading-induced fraction (active rebalancing) and a priceinduced fraction (passive rebalancing). Straightforwardly, the trading-driven (price-driven) change is obtained by keeping prices (holdings) unchanged for the three-month period between two consecutive reporting dates.

Figure 2 plots the overall quarter-to-quarter change in local bias, as well as the proportions attributable to active and passive rebalancing, respectively. Interestingly, we observe that the transactions-based effect and the performance-based effect work in opposite directions for nearly all quarters. In other words, including price changes understates rather than overdraws individuals’ active decisions to shift their portfolio weights. While usually low, this attenuation is particularly pronounced around the peak of the financial crisis in the third quarter of 2008, where active rebalancing without price effects would have resulted in considerably higher local bias levels. We conjecture that for individual investors―unlike, say, fund managers―the absence of trading does not reflect a deliberate portfolio strategy. Thus, we are concerned with active rebalancing decisions and focus on trading-induced changes in local bias in the following.

5.3 Results

Our findings clearly support a flight to familiarity among German individual investors. Figure 3 plots the development of the VDAX New against the respective local bias levels for the period under review. As can be seen, we document a strong congruence between expected stock return volatility and local bias over time. We regress the local bias on the VDAX New to examine whether the relationship illustrated in Figure 3 proves statistically significant.

Note that, in order to do so, we use first differences of the two series since the levels turn out to be non-stationary processes of order one. We also include an AR(1)-term to mitigate possible autocorrelation and thereby bring the Durbin-Watson statistics close towards the required

2. Finally, we alter the baseline regression (Regression 1) by adding the first lag of the VDAX New change to capture potential inertia of households in their reaction upon a change in stock market uncertainty (Regression 2). Table 7 reports our results. Corroborating the initial evidence from Figure 3, we find that changes in the VDAX New turn out to be highly significant in explaining adjustments in local bias levels among private households. Specifically, a ten percent rise of the VDAX New translates into an average increase in local bias of as much as

0.6 percent. Results with regard to the lag-one VDAX New change (Regression 2) are not statistically significant, indicating that households adjust their portfolios in the same quarter in which the change in stock market uncertainty takes place.

Interestingly, not only do we observe a flight to familiarity in times of stock market downturn, but also a reversal of this effect as soon as stock prices pick up again: when markets rebound from mid-2009 on, local bias levels also decrease significantly as a result of this development. By the end of 2009, local bias levels have almost reached pre-Lehman levels. We further sort out the relation of market performance and local bias by calculating the quarterly changes in German stock market performance for our period under review and assigning the 16 values we obtain into four quartiles according to magnitude of change. As a performance measure, we use the broad CDAX index. The average change in CDAX levels per quartile, together with the corresponding mean local bias level, is reported in Table 8. Consistent with what we observe in Figure 3, we find that for pronounced upward or downward moving markets in particular, changes in stock market performance and local bias of German household investors are strongly negatively correlated.

Next, we are interested in whether the portfolio rebalancing towards familiar (local) stocks which we observe in times of economic uncertainty is the result of a few households tilting their portfolios heavily towards nearby stocks or―on the contrary―a widespread trend among private investors. To this end, we look at the average portfolio shift of private households aggregated at the bank level and sum up the number of mean increases and mean decreases in trading-based local bias, respectively.

Table 9 reports our results. In most quarters, we see that increases in overall local bias levels are indeed accompanied by increased average exposure to nearby companies for the greater part of banks, and vice versa. While this relation is stronger in the second half of the sampled period starting shortly before the financial crisis, we conclude from our data that the flight-to-familiarity effect is driven by the majority of individual investors. Interestingly, we see widespread shifts towards local equity following two events which private investors associate particularly strongly with the outbreak of the financial crisis. Specifically, the collapse and firesale of Bear Stearns in mid-March 2008 was followed by a 3.4% increase in local overinvestment, and―most prominently―, the bankruptcy of Lehman Brothers later that year on September 15 subsequently lead to a 6.4% jump in individual investor’s local bias. Also, Table 9 documents shifts towards geographically close companies in the second quarter of 2006, when the DAX dropped by ten percentage points in less than one month during May

2006. Analogously, the flight to familiarity reverses in 2009 and average increases in local equity reach their lowest levels in mid-2009 when newsflow has again become positive across the board and several important economic indicators reach their pre-Lehman levels.

Taken together, we find (i) that individual investors pull out of remote (unfamiliar) stocks, and pour into local (familiar) stocks during times of financial crises, (ii) that this flight to familiarity is driven by active portfolio rebalancing and rebounds when the economy picks up again, and, finally, (iii) that this shift is a robust phenomenon across the majority of individual investors.

Given this evidence, there is reason to assume that the concept of investor familiarity induced by ambiguity aversion might be a promising avenue in the attempt to explain the local bias phenomenon among individual investors. One can reasonably assume that private households do not devote their entire time and energy to collecting and processing all information available in the market. Put differently, due to time (and other) constraints, it is unrealistic to conjecture that people are equally ambiguous about all securities. Rather, they possess different degrees of ambiguity across different securities, as modeled by Boyle et al. (2011), and favor investments which they are less ambiguous about. In addition to that, portfolio choices are characterized by several distinct features which may aggravate investors’ ambiguity aversion. On the one hand, asset allocation decisions are situations in which different chances are compared against each other instead of being evaluated separately. In such settings, people are particularly inclined to exhibit intolerance towards the uncertain (Fox and Tversky, 1995). On the other hand, investment choices are decisions where the majority of households judge themselves to be relatively less competent; this matches the findings of Heath and Tversky (1991), who demonstrate that ambiguity aversion is especially pronounced when people find it difficult to assess a set of prospects. Consequently, local bias seems to be part of a larger phenomenon in which individual investors show a preference for the familiar which is attributable to ambiguity aversion. Investors’ aversion to risk implies that their portfolios should be diversified, but―being ambiguity averse―they trade off a piece of this diversification by overweighting familiar assets in their stock portfolios, thereby creating a local bias.

6 Conclusion

This paper contributes to the literature on the geography of investment. We investigate the role of individual investors’ location for their stockholdings. Analyzing a rich data set which covers the accounts of nearly six million private households in Germany, we find strong evidence for a local bias―i.e. an overweight of geographically close versus remote German companies in their equity portfolios―and investigate the reasons for this portfolio concentration. We consider two possible explanations. On the one hand, it could be that the overweight in nearby stocks reflects informed investment decisions. In this case, a locally biased portfolio would not necessarily constitute an investment mistake. Instead, it could still be consistent with traditional mean-variance portfolio theory in case the increased portfolio risk incurred through the regional focus is rewarded by a superior performance of the local stockholdings.

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