1 Subjective Evaluation Of Delayed Risky Outcomes: An Experimental Approach Uri Benzion a, Jan Pieter Krahnen b, Tal Shavit c a Department of Economics, Ben-Gurion University, Beer-Sheva, b Department of Finance, Goethe Universitaet Frankfurt, Germany. c Department of Management and Economics, The Open University of Israel

2 This Study Examines experimentally the subjective evaluation of delayed risky lotteries and derives the implied behavior of discount rates and risk premium that agents use in their evaluations. We use evaluation tasks in two positions (WTP and WTA).

3 In points: (1)We test two alternative approaches to evaluate delayed lotteries. The financial valuation approach (FVA) and The certainly equivalent approach (CEA). (2) We examine the existence of hyperbolic discounting function (3) Compare the time discounting for certain and uncertain amounts.

4 One formula that yields a hyperbolic discount function for a given lottery is Where β, 0<ß<1, is the constant rate for one period. = Hyperbolic and Jump functions

5 We will use a slightly more general formulation in our analysis that allows to determine the extent of the jump in t=0 separate from the slope of the discount function after t=0. This “jump discount” function is described by (the same for Bond): In the cross section, the jump of the discount function is inversely related to the face value of the asset = For example

6 Experiment1- Procedure The participants in the experiment were 64 undergraduate students of Economics. In the instructions, subjects were told that the assets would be sold and bought from them using the second-price auction The auctions were presented in a random order to avoid any order effect. We asked the subjects: (a) To bid the maximum price they are willing to pay (WTP) today for a lottery or a sure amount in different times (b) Ask the minimum price they are willing to accept today for a lottery or a sure amount they own in different times (WTA). The payment from an asset subjects won, was made at the time of realization of the asset. For example, if the subjects won a lottery in 4 weeks the payment was 4 weeks after the experiment

7 The Assets The Lottery pays 100 with probability 60%, and 25 otherwise (The expected value is 70), and the bond’s face value is 70 (as the lottery expected value). The auctions included current bidding and asking prices for present and future assets.

8 Expected ValueRealization TimePayment Asset 70Today Lottery 701 WeekToday 704 WeekToday 708 WeekToday 701 WeekToday Fixed sum 704 WeekToday 708 WeekToday Table 1 – The assets

9 Experiment 2 (1995) In all the problems the subjects were asked to buy bond with different size and different time to maturity. The risk attitude was measured by the time zero lottery.

10 Findings – Table 2

11 The results reject the FVA hypothesis and support the CEA hypothesis, meaning constant risk premium.

12 Using the Wilcoxon Signed Ranks Test, we found that the forward weekly time discount between 1 week and current time is the highest (p < 0.05), while no significant difference was found between the other periods. Subjects discount heavily the first week and by small but constant weekly discount rate discount the next weeks. Table 3 – discount per week

13 The table shows that the lottery’s weekly time discount is lower than the bond weekly time discount for the buying position (p-value =<0.05). The results are consistent with Keren and Roelofsma (1995) and Anlbrecht and Weber (1997). The implicit discounting for uncertainty overlap with delay discounting. Alternatively, We use the anticipation effect. The anticipation effect (Loewenstein 1987) describes additional utility (disutility) associated with delayed consumption of desirable (undesirable) good.

14 The results from experiment 2 Discount Rate = – *Asset size *(t-1) – *(RA) (0.00) (0.014) (0.00) (0.75) Risk attitude is not significant. (As opposed to hypothesis 6) Each period increase the discount rate by 0.45%. An increase of 100 DM in the asset size reduces the discount rate by 0.46%. The meaning is that the jump reduces by 0.46% for 100 DM (as we expected in hypothesis 7)

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16 In another regression we gave each amount dummy variable (we had 10 different amounts) Not all the dummies are significant. The risk attitude is not significant. We present the graph, which connect the jump and the amount:

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18 Summary The finding about the Jump increase our doubt about the hyperbolic function. Frederic, et al (2002) who claim that if anticipatory utility motivates one to delay consumption more than one otherwise would, the imputed discount rate will be lower than the true degree of time preference.

19 this work show the effect of “implicit discounting for uncertainty” for evaluation tasks ( Buying and selling) and not for choice task as in past research. The first period high discount equation explain the results better than the hyperbolic equation. No effect of risk aversion on time discount. No change in Endowment effect for delayed lotteries and Bonds.