An investor has a sum of money to invest.

He can either:

Keep it in a savings account (gain 20 per year)

Or buy shares with equal probabilities each year of his investment gaining 500 or losing 250

The investor has a linear value function but he is loss-averse, i.e. v(z)=z for z0 v(z)=z for z1)

If = 2.5 and his investment horizon is one year, which prospect does he choose? What if his horizon is two years? (For simplicity assume returns are additive, not compound.)