Topic 3
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

Topic 3 PowerPoint PPT Presentation


  • 145 Views
  • Uploaded on
  • Presentation posted in: General

Topic 3. Prices, Returns & Trading Costs. Returns Measurement. Prices (P). P 0 , P 1 , P 2 , … , P T. Time. P 0. P 1. P 2. P T. Arithmetic Returns ( P). P 0,1 = P 1 – P 0 P 1,2 = P 2 – P 1 P T-1,T = P T – P T-1. Percentage Returns (r).

Download Presentation

Topic 3

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Topic 3

Topic 3

Prices, Returns & Trading Costs


Topic 3

Returns Measurement


Topic 3

Prices(P)

P0 , P1 , P2 , … , PT

Time

P0

P1

P2

PT


Topic 3

Arithmetic Returns (P)

P0,1 = P1 – P0

P1,2 = P2 – P1

PT-1,T = PT – PT-1


Topic 3

Percentage Returns (r)

r0,1 = ( P1 – P0 ) / P0= P0,1 / P0

r1,2 = ( P2 – P1 ) / P1= P1,2 / P1

rT-1,T = ( PT – PT-1 ) / PT-1= PT-1,T / PT-1


Topic 3

Price Relatives (PR)

PR0,1 = P1 / P0 = ( P0 + P0,1 ) / P0=1 + r0,1

PR1,2 = P2 / P1 = ( P1 + P1,2 ) / P1= 1 + r1,2

PRT-1,T = PT / PT-1 = ( PT-1 + PT-1,T ) / PT-1 = 1 + rT-1,T

PR0,T = PT / P0 = (P1 / P0) * (P2 / P1) *…* (PT / PT-1)


Topic 3

Log Returns (R)

R = ln(1+r) = ln(price relative)

R0,1 = ln(P1/P0)= ln(P1) – ln(P0) = ln(1+r0,1)

R1,2 = ln(P2/P1) = ln(P2) – ln(P1) = ln(1+r1,2)

RT-1,T = ln(PT) – ln(PT-1) = ln(1+rT-1,T)

PR0,T = PT / P0 = (P1 / P0) * (P2 / P1) *…* (PT / PT-1)

R0,T = R0,1 + R1,2 +…+ RT-1,T =

Ri-1,i = ln(PT) – ln(P0)


Topic 3

Question:

Which of the following may be normally distributed?

P

r

PR

R


Topic 3

Two Period Log Returns

P2 = P0 ( 1 + r0,2 )

P2 = P0 ( 1 + r0,1 ) ( 1 + r1,2 )

1 + r0,2 = P2 / P0 = ( P1 / P0 ) * ( P2 / P1 ) =

= ( 1 + r0,1 ) ( 1 + r1,2 )

R0,2 = R0,1 + R1,2


Topic 3

P* Returns in TraderEx

  • When P* follows a random walk, P* returns are generated by draws from two distributions:

  • Poisson distribution (when does P* jump)

  • A lognormal distribution (how big is the jump)

  • Ln(P*t ) = Ln(P*t-1 ) + Rt

the jump


Topic 3

Means and Variances


Topic 3

Log Returns: Two Period Mean

Assume a constant Mean:

E(R0,1) = E(R1,2)

E(R0,2) = E(R0,1) + E(R1,2)

E(R0,2) = 2E(R0,1)


Topic 3

Log Returns: Two Period Variance

Var(R0,2)=Var(R0,1)+Var(R1,2)+2Cov(R0,1,R1,2)

Assume a constant Variance:

Var(R0,1) = Var(R1,2)

For Cov(R0,1,R1,2) = 0

Var (R0,2) = 2 Var(R0,1)

What if Cov(R0,1,R1,2) < 0 ?


Topic 3

Costs


Trading costs

Trading Costs

1.Explicit costs

  • commissions

  • taxes

  • etc.

    2.Execution Costs(the implicit costs of trading)

  • Bid-ask spread

  • Market impact

  • Delay/opportunity cost

  • Implementation shortfall


Topic 3

From Trading Costs to Volatility

  • The bid-ask spread

  • Market impact

  • Momentum trading

  • Imperfect price discovery

Trading costs

cause prices to bounce between higher and lower values


Topic 3

Price

Time

Trading Costs & Volatility

C

= Implicit transaction cost of buy or sell

= Transaction price (triggered by buy order)

= Transaction price (triggered by sell order)

= Magnitude of C

= Unobserved, costless trading price

P*

P*


Topic 3

Trading Costs & Volatility

C

= Implicit transaction cost of buy or sell

= Observed price of buy-triggered trade

= Observed price of sell-triggered trade

= C

= Unobserved, costless trading price

P*

Price

P*

Time


Topic 3

Trading Costs & Returns

Price

P

T

Time


Topic 3

Which is More Volatile?

P* or

the transaction price that we observe?

Price

P*

Observed

Transaction

Price

Time


  • Login