Issues of Behavioural Finance - Assignment Example

From the maximization equation ii, find the First order condition of consumption period 1 as shown below. As shown in iii, after computing the unknown values with the know values you find the present value of CHF as shown in iv. The subsequent years are computed by referencing their formulas with respect to the known Co. The exponential discounting graph has a positive slope due to its positivity index.

Inter-temporal utility function
U(C_0,C_1,C_2 )=lnC_0+β(δlnC_1+δ^2 lnC_2)
U(C_0,C_1,C_2 )=lnC_0+0.5βlnC_1+0.25βlnC_2)---i
max U=lnC_0+0.5βlnC_1+0.25βlnC_2 s.t C_0+C_1+C_2=A_1) ----ii
FOC is 1/C_0 =λ---iii
0.5β/C_1 =λ
0.25β/C_2 =λ

This implies C_0=2/β C_1=4/β C_2=λ=βC_0=2C_1=〖4C〗_2
C_0+0.5βC_0+0.25〖βC〗_0=A_1
=C_0+0.75βC_0=A_1
C_0=A_1/((1+0.75β) )=C_1=C_2=(βA_1)/(1+0.75β)
C_0=100/(1+0.75*0.6)
=100/5.5
=18.18 CHF---iv

For the second period
0.5β/C_1 =λ
0.25β/C_2 =λ

Plugging into the 100CHF, we will have
1/0.75 C_1+C_1=0.75*18.18
=(7/3) C_1=13.635*3/7
=5.843 CHF

The third period will be
1/0.75 C_2+C_2=0.75*18.18
=(7/3) C_2=13.635+0.6*3/7
=3.506 CHF
The graph for the present exponential discounting has a positive slope while the graph for the standard exponential discounting is flat.

Question 2
U(C_0,C_1,C_2 )=lnC_0+β(δlnC_1+δ^2 lnC_2)
U(C_0,C_1,C_2 )=lnC_0+0.5βlnC_1+0.25βlnC_2)
max U=lnC_0+0.5βlnC_1+0.25βlnC_2 s.t C_0+C_1+C_2=A_1)
FOC is 1/C_0 =λ
0.5β/C_1 =λ
0.25β/C_2 =λ

This implies C_0=2/β C_1=4/β C_2=λ=βC_0=2C_1=〖4C〗_2
C_0+0.5βC_0+0.25〖βC〗_0=A_1
=C_0+0.75βC_0=A_1
C_0=A_1/((1+0.75β) )=C_1=C_2=(βA_1)/(1+0.75β)
C_0=244/(1+0.75*0.6)
=244/5.5
=44.36 CHF

For the second period
0.5β/C_1 =λ
0.25β/C_2 =λ

Plugging into the 244CHF, we will have
1/0.75 C_1+C_1=0.75*44.36
=(7/3) C_1=33.27*3/7
=14.26 CHF

The third period will be
1/0.75 C_2+C_2=0.75*44.36
=(7/3) C_2=14.26*0.6
=8.556 CHF

Question 3
In period 1, the consumer would have 100 – 18.18 = 81.82
0.5β/C_1 =λ
0.25β/C_2 =λ

Plugging into the 100CHF, we will have
1/0.75 C_1+C_1=0.75*81.82
=(7/3) C_1=61.365*3/7
=26.30 CHF

The second period will be
1/0.75 C_2+C_2=61.365
=C_2=61.365*0.6
=36.82 CHF
The value does not implement what he planned to do at time zero.

Question 4
This person should sign an agreement in period zero due to the income effect and substitution effect. The high-interest rate increases income for a certain amount of time. Therefore, an increase in consumption during the first and second periods makes the income effect of the borrower to be negative in the period. Additionally, due to the substitution effect, the gross interest rate is relative to consumption price during period zero compared to periods 1 and 2 (Nielsen, 2005). Hence, it will be more expensive in the first and second periods compared to period zero. As such, for a person, a rise in interest rate in the first or second period may raise or reduce the rate during period zero.

Optional Problem Set 2
Question 1
Assuming that Mr. Spout has an expected payout of $1 when he invests in stock A, Mr. Spout will not choose the guaranteed stock A. The stock has an expected uncertainty of 1/3; therefore, Mr. Spout will take his chances and invest in stock B. He will not have a preference between investing in either stock A or investing in stock B (Forbes, 2009). To state this in a different way, Mr. Spout will later select the investment that has a higher expected return. Mr. Spout will invest in stock B in the future since he does not consider taking into account the investment risk in his decision. As a Bayesian learner, Mr. Spout's decision will be influenced by uncertain knowledge and the time is linked through the process of learning of the stocks.

Question 2
As a risk-neutral investor, Mr. Spout will be indifferent between investing in stock A or in Stock B. Since he has experience in stock A, Mr. Spout will invest in stock B. As a Bayesian investor, Mr. Spout experimented in the first period and observed the results. Therefore, he will invest in stock B due to its uncertainty element attached to the stock. He will not have a preference between investing in either stock A or investing in stock B. To state this in a different way, Mr. Spout will later select the investment that has a higher expected return. Mr. Spout will invest in stock B in the future since he does not consider taking into account the investment risk in his decision. As a Bayesian learner, Mr. Spout's decision will be influenced by uncertain knowledge and the time is linked through the process of learning of the stocks (Nielsen, 2005).

Question 3
a)
As a reinforcement learner, Mr. Spout will still invest in stock A that previously had a return of $1. In reinforcement learning, the investor repeats his behavior that coincided with the previous experience. Here, Mr. Spout will extrapolate his personal experience when making his investment decision.

b)
After receiving $0 after investing in stock A Mr. Spout will shift his investment to stock B. As a reinforcement learner, he will repurchase stock if and only if he realized a positive return. Here, the investors are more likely to buy stocks if their investment in the industry had a higher return (Forbes, 2009).

Question 4
Reinforcement Learners and Bayesian Learner behave similarly. This is because, in both, the investor is placed in a setting and is required to behave optimally in that environment. Their actions are non-deterministic and initially unknown and need learning (Redhead, 2008). Read More