Chapter 6. Mean-Variance Portfolio Theory || Part 1

주식이란?

• Stocks represent a fraction of ownership in a business
  주식은 사업체의 소유권의 일부를 나타냅니다

• A single share of the stock represents fractional ownership of the corporation in proportion to the total number of shares

Portfolio Management

• Our goal : Form the best portfolio among various assets
• How are we going to decide which portfolio is the best?
  • ==> We will consider two measures: Portfolio return and risk
• portfolio의 return과 risk를 어떻게 계산하느냐?
  • 개별 주식들의 return을 통해서 계산한다. 
  • But it is difficult because we are not sure which stocks will go up and which stocks will go down
  • However, returns are not completely random because historical movements provide some information
  • We can use the mean (expected value), variance, and covariance of stock returns

6.1 Asset Return

Asset Return

• Asset(자산) : 자주 사고 팔 수있는 투자 수단
• Rate of Return

Portfolio

• Suppose now that n different assets are available

• We can form a master asset or portfolio of these n assets
• 주식마다 쪼개서 다른 금액을 투자할 수 있음(만약 short투자가 가능하면 음수도 됨)

 

• Amounts invested can be expressed as fractions of the total investment

• where w_i is the weight or fraction of asset i in the portfolio
  특정 주식 i에 얼마나 투자했냐를 전체 투자 금액에 가중치(w)를 할당함으로써 표기할 수 있음
• 당연히 weight들의 합은 1이다. 

Portfolio Returns

• Let R_i denote the total return of asset i

• Amount of money generated at the end of the period by the ith asset is

• Total amount received by this portfolio at the end of the period is

• Overall total return of the portfolio is

• 개별 주식에 투자한 가중치 * 전체 투자 금액 * 개별 주식의 수익률 = 개별 주식의 return이 된다. (사실 당연한 이야기)

 

• 개별 주식 수익

개별 주식 수익

• 전체 수익

전체 수익

• overall total return of portfolio

• R은 투자 금액을 몰라도 알 수 있다, 투자 비율만 알면 산출 가능하다. 

• Return을 곱하는 게 아니라, Rate of return(r_i)를 곱해도 똑같다. 

Short Sales(공매도) 1

• Short selling or shorting: Process of selling an asset that you do not own
  • Borrow the asset from someone who owns it (such as a brokerage firm)
  • Then sell the borrowed asset to someone else, receiving an amount X_0
  • At a later date, you repay your loan by purchasing the asset for X_1 and return the asset to your lender
  • If the later amount X_1 is lower than the original amount X_0, you will have made a profit of (X_0 - X_1)
  • Short selling is profitable if the asset price declines

 

Short Sales(공매도) 2

• Short selling is considered risky (even dangerous) by many investors

• Potential for loss is unlimited
• If the asset value increases, the loss is X_1 - X_0. but X_1 can increase arbitrarily (so can the loss)