dse 2010

[SHIKHA]

Suppose there is only one future period and (the presently unknown) state of the world in that period can be either s1 or s2. The future return on a share of a given company is 5 in state s1 and -1 in state s2. The future return on a government bond is independent of the state. Suppose a third asset is offered on the market whose return is 3 in state s1 and 0 in state s2. The current prices of the stock and the bond are 3 and 1 respectively. If the price of the new asset rules out the possibility of any arbitrage profit, what is the price of the new asset?
a. It depends on probabilities of the future states
b. Strictly between 2 and 3
c. Strictly between 1 and 2
d. 2

plz help amit sir....
i know its being solved in earlier posts...bt i m nt able to understand ....help!!!!

[s]

hey this is what i did;

the expected return from a share of company is 5*s1+(-1)*s2
now to make people invest in this share company must set price of share such that its less than or equal to the expected return ie 5*s1+(-1)*s2>=3  if price is above expected return no one vil buy it..and also optimal for co is to set 5*s1+(-1)*s2=3 as ths gives max profit for co..
and for govt bond expected return is 1*s1+1*s2 and same logic applies that govt vil set price which shuld be equal to expected return ie 1*s1+1*s2=1

solve these two simultaneouly we get s1=2/3

now for third asset again price equals exp return so 3*s1=x , let x be price of third asset
thus x=3*2/3=2

[SHIKHA]

HEY UR METHOD IS NT CORRECT COZ ...THE QUES SAYS EITHER S1 OR S2 FUTURE PERIOD CAN ONLY EXIST..

[anon_econ]

they r the probabilities of the 2 states of the world

[lovekesh]

"S" has solved it correctly but i think why the share price is equal to 3 is not bcoz firm is maximizing it's profit by pricing it at 3. Firms don't set the price of their stock, market does. it's just that in stock market, share price reflects everything we know about that particular share. In this case, it's expected return. Everybody has information about the possibilities of future states. So, today market price will be equal to expected return.