Suppose you find the following information for Tesla stock $($TSLA$)$:

$$ The minimum margin requirement $=30\%$

$$ Current stock price $=$ $$50$ per share

$$ No dividend is expected within a year

$$ The interest rate on a margin loan is $6\%$ per annum

You have an assessment of the TSLA price probability distribution next year as below:

Bear Market Normal Market Bull Market

Probability $0\mathrm{.}20\mathrm{.}50\mathrm{.}3$

TSLA price $455566$

You bought $600$ shares of the stock with $$15,000$ of your own funds.

a$)$ What would be your rate of return on this investment if you sell the stock for $$62\mathrm{.}50$ one year later? $(9$ pts$)$

b$)$ What would be the stock price when a margin call occurs $($assuming you don$$t pay any interest on the margin loan$)?(9$ pts$)$

c$)$ What is the rate of return of your investment if the price in one year is as predicted by the probability distribution above?

$(10$ pts$)$

d$)$ What are the expected return and standard deviation of the stock, respectively? $(12$ pts$)$