We suppose a financial market with three assets: a riskless asset B and two risky funds S and T. The continuous free rate is equal to 3%. The investment fund S has a continuous mean return of 6% and a volatility of 20%; the investment fund T has a continuous mean return of 8% and a volatility of 25%. The returns of the two funds are supposed to be cor with a correlation coefficient of 25%.
A bank proposes to its client a guaranteed product of maturity 2 years with a fixed annual return equal to 3.2 %.
The initial deposit of the clients is equal to 100,000 €.
The bank could invest this deposit following 4 possible dynamic strategies: S1 : all in the risk free asset
S2 : all in the risky asset S
S3 : 50% in S and 50% in T
S4 : 1/3 in each asset .
Compare and comment for these 4 strategies the level of initial equity to bring by the shareholders in each of the following regulatory situations:
a) Use of Value at risk with a safety level of 99%
b) Use of the Tail Value at risk with a safety level of 97%
c) Use of the standard deviation principle with a lambda equal to 2.5 d) Full Hedging with derivatives.
In terms of cost for the shareholders, what is the main difference between on the one hand situations a) b) c) and on the other hand situation d)?

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