Lump sum or averaging?

(a) Prove Proposition 6B.6.2. (b) An investor has ₹24 lakh. The equity fund's expected return is 0.9% a month and cash earns 0.45% a month. Compare the expected terminal wealth after 24 months of investing at once with that of investing ₹1 lakh a month (the rest in cash). (c) Find the fraction $\theta$ that, invested in equity at the start and held for 24 months with the rest in cash, gives the same expected terminal wealth as the averaging plan. Interpret. (d) Summarise Constantinides's (1979) argument in your own words.