INVESTMENTS I vIClLlELI aSSer aind rrorrler porrolIos a Definition: the marginal return-to-risk ratio (RRR)of risky asset i in a portfolio p is RRR-marginal return or, /Ow E marginal risk do. law a Claim: for any frontier portfblio'p, the return-to-risk ratio of all risky assets must be the same RRR=i -RRR =P ip p a Just because Sharpe ratio of the frontier portfolio can not improved
INVESTMENTS Individual asset and frontier portfolios Individual asset and frontier portfolios Definition: the marginal return-to-risk ratio (RRR) of risky asset i in a portfolio p is: Claim: for any frontier portfolio p, the return-to-risk ratio of all risky assets must be the same: Just because Sharpe ratio of the frontier portfolio can not improved ip p i f p i p i i r r w r w m inal risk m inal return RRR σ / σ /σ / arg arg − = ∂ ∂ ∂ ∂ = = p p f p ip p i f i r r RRR r r RRR σ σ σ − = = − = /
INVESTMENTS Alternatiye cal e(r) CAL (P)CAL(A) dddddddddddd_d d』』』dd CAL (Global w minimum variance r G PP&f m a&f
INVESTMENTS Alternative Alternative CALs M E(r) CAL (Global minimum variance) CAL (P) CAL (A) P A F P P&F A&F M A G P M
INVESTMENTS n important formula ■ Rewriting a We have the following important results Where is the beta of asset i with respect to a frontier portfolio p a We can interpret the above relation as follows Given any frontier portfolio p(except the risk-free asset) Bip gives a measure of asset i's systematic risk r gives the premium per unit of systematic risk he risk premium on asset i equals the amount of its systematic risk times the premium per unit of the risk
INVESTMENTS An important formula An important formula Rewriting We have the following important results Where is the beta of asset i with respect to a frontier portfolio p. We can interpret the above relation as follows: Given any frontier portfolio p (except the risk-free asset) gives a measure of asset i’s systematic risk. gives the premium per unit of systematic risk. the risk premium on asset i equals the amount of its systematic risk times the premium per unit of the risk. p p f ip p i f r r r r σ σ σ − = − / ( ) ( ) 2 p f ip p f p ip i f r − r = r − r = β r − r σ σ 2 / βip = σ ip σ p βip p f r − r
INVESTMENTS Main points of modern portfolio theory a 1. Investors hold frontier portfolios a 2 Investors are concerned only with portfolio risk a In this chapter, we study how investors asset demand determines the relation between risk and return of assets in a market equilibrium---a model to price risky assets a The task for us now is to identify a frontier portfolio, which would give us a pricing model
INVESTMENTS Main points of modern portfolio theory Main points of modern portfolio theory and CAPM and CAPM 1. Investors hold frontier portfolios 2 Investors are concerned only with portfolio risk. In this chapter, we study how investors’ asset demand determines the relation between risk and return of assets in a market equilibrium---A model to price risky assets. The task for us now is to identify a frontier portfolio, which would give us a pricing model
INVESTMENTS The market portfolio Definition: the market portfolio is the portfolio of all risky assets traded in the market Definition: the market value(capitalization)of an asset is its total market price, i. e, the price one has to pay to buy all of it. Debt, A-share, B-share of a company) MCAPi(price per share)i*(# of shares outstanding )i a The total market capitalization of all risky assets is MCAP=∑MCAP a The market portfolio is the portfolio with weights in each risky asset I being MCAP MCAP
INVESTMENTS The market portfolio The market portfolio Definition: the market portfolio is the portfolio of all risky assets traded in the market. Definition: the market value (capitalization) of an asset is its total market price, i.e., the price one has to pay to buy all of it.(Debt, A-share,B-share of a company) MCAPi=(price per share)i*(# of shares outstanding)i The total market capitalization of all risky assets is The market portfolio is the portfolio with weights in each risky asset i being ∑= = n i MCAPm MCAPi 1 ∑= = n j j i i MCAP MCAP w 1