{'fraction_non_alphanumeric': 0.03113941967445152, 'fraction_numerical': 0.008492569002123142, 'mean_word_length': 4.966244725738397, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An Asset Allocation Sub-Puzzle

This paper documents a sub-puzzle in asset allocation. Canner, Mankiw and Weil (1997) point out that empirically the ratio of bond to stock holdings of a typical investor varies with her risk-averse attitude. This observation directly challenges the well-known mutual fund separation theorem of Tobin (1958) and Markowitz (1952). This paper reports additional evidence on investor's portfolio choice, finding that not only does the bonds to stocks ratio change, but within the stock portfolio, the ratio of high-risk stocks to low-risk stocks also changes with an investor's risk tolerance. This finding is important because most current literature attempts to solve the asset allocation puzzle by applying different interest rate models. Our finding shows that the puzzle involves more than just about interest rates, and needs a more fundamental examination from the perspective of an investors' risk attitude. Drawing on the loss aversion literature, we propose a general model that can solve both the Canner-Mankiw-Weil puzzle and the sub-puzzle. The key is that investors are loss averse and care about their expected worst-case returns. When an expected worst-return constraint is added to investors' utility maximization, the optimal ratio of low-risk to high-risk assets, be it bonds to stocks or low-risk stocks to high-risk stocks, changes with investors' risk attitudes.