Tutor profile: Abhay R.
Explain the concept of diversification of portfolio and how the diversification benefits change with change the value and magnitude of the correlation between the assets in the portfolio in case of portfolio formed out of two assets.
The variance of the return of portfolio can be reduced by including additional assets in the portfolio a process referred to as diversification.-->”Don’t put all your eggs in one basket”. The process of spreading an investment across assets (and thereby forming a portfolio) is called diversification. The diversification benefits are maximum when the two assets are negatively correlated in comparison to when the assets are positively correlated. As is elaborated below The tendency of the returns on two assets to move together. If the returns on two assets tend to move up and down together, we say they are positively correlated. If they tend to move in opposite directions, we say they are negatively correlated. If there is no particular relationship between the two assets, we say they are uncorrelated. Let: σ12: is the covariance between the two assets under the portfolio ρ: the covariance between the two assets under the portfolio σ1: is the standard deviation for the asset 1 σ2: is the standard deviation for the asset 2 w1: is the weight(i,e proportion of money spent) assigned to asset 1 w2: is the weight(i,e proportion of money spent) assigned to the asset 2 Using σ12 = ρ σ1 σ2 The RIsk or Variance of the portfolio formed out of two assets is given by Variance of Portfolio = (w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 + 2w1 w2 σ12 = (w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 + 2w1 w2 ρ σ1 σ2 Case I Correlation ρ =1 i.e assets are perfectly positively correlated Variance of Portfolio = (w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 + 2w1 w2 ρ σ1 σ2 = [w1 σ1 + w2 σ2)]^2 Maximum variance(risk) when the assets are perfectly positively correlated Case II Correlation is ρ = - 1 i.e they are perfectly negatively correlated Variance of Portfolio =(w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 - 2w1 w2 ρ σ1 σ2 = [w1 σ1 - w2 σ2)]^2 Minimum variance(risk) when the assets are perfectly negatively correlated.The portfolio risk can be completely diversified away(i.e zero risk) in case the assets are perfectly negatively correlated for the given specific weight assigned to the two assets under the portfolio. w1+w2 = 1 w2= 1 - w1 substitute this above we get Variance of Portfolio = [w1 σ1 - (1- w1)σ2]^2 The above variance term can be zero when w1 σ1 - (1- w1)σ2 = 0 w1 σ1+w1 σ2 - σ2 =0 w1 ( σ1+σ2) = σ2 w1 = σ2 / ( σ1+σ2) w2= 1- w1 = 1-σ2 / ( σ1+σ2) =σ1 / ( σ1+σ2) For a specific value of weights i.e for w1=σ2/( σ1+σ2)) and w2=σ1/(( σ1+σ2)) variance of the portfolio can be reduced to zero( i.e risk can be completely diversified away in case of a portfolio of 2 assets when these two assets are perfectly negatively correlated i.e ρ = - 1. So minimum variance when the assets are perfectly negatively correlated CaseIII: When the correlated -1 < ρ < 1 Variance of Portfolio = (w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 + 2w1 w2 ρ σ1 σ2 Case IV: When the correlation is zero ρ=0 Variance of Portfolio=(w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 From above we can write [w1 σ1 - w2 σ2)]^2 < (w1)^2 (σ1)^2 + (w2)^2 (σ2)^2 + 2w1 w2 ρ σ1 σ2 < [w1 σ1 + w2 σ2)]^2 This inequality tells that risk(variance) of the portfolio is least when the assets are perfectly negatively correlated and risk is maximum when the assets are perfectly positively correlated.
Define impossible trinity and explain how the nations can utilize the monetary policy and fiscal policy in case of perfect capital mobility and fixed exchange rate regimes.
Impossible trinity refers to the policy dilemma where the policy-makers can’t simultaneously attain three objectives of independent monetary policy, fixed exchange rate, and have perfect capital account convertibility. If policy-makers opt for perfect convertibility on the capital account then they have to make a choice between having o fixed exchange rate or maintaining the independent monetary policy. Case: Perfect capital mobility and fixed exchange rate regime With perfect capital mobility balance of payment(BOP) curve is horizontal as a small difference in domestic interest rate wrt foreign interest rate leads to a huge amount of capital mobility, this leads to equality between the domestic and foreign interest rates. In this case, if policymakers try to increase the output in the economy by using expansionary fiscal policy then the IS curve shifts to the right. As the IS curve shifts to the right, it intersects the LM curve at a point above the BOP curve. For points above the BOP curve, the domestic interest rate is higher than the foreign interest rate leading to capital inflow. As under fixed exchange rate central bank stands ready to buy or sell foreign currency in order to keep the exchange rate fixed, so the inflow of capital central bank takes the foreign currency and supply the domestic currency in exchange. With an increase in the supply of money LM curve shifts rightward. The intersection of the new LM curve and the IS curve gives a higher level of output in comparison to the initial level of output. This means that fiscal policy is an effective tool to raise the level of output under a fixed exchange regime with perfect capital mobility. In this case, if policymakers attempt to raise the output level by following the independent expansionary monetary policy then this policy leads to a shift in the LM curve to the right. The new LM curve intersects the IS curve to the point below the BOP curve. FOr points below the BOP curve, the domestic interest rate is lower than the foreign interest rate this leads to capital outflow under perfect capital mobility. For capital outflow, the central bank in order to keep the exchange rate fixed, supply the domestic currency in exchange for the foreign currency. This results in a reduction of money supply leading to backward shifting of the new LM curve till the point it reaches to old LM curve and output level in economy return to the previous level. So independent monetary policy is an ineffective tool to raise the level of output in the economy under the fixed exchange system with perfect capital mobility. In conclusion: Unde fixed exchange rate with perfect capital mobility: monetary policy is completely ineffective(monetary independence of the central bank is lost) and fiscal policy is completely effective in raising the level of output in the economy.
Ques: Why does monopolist not operate on the inelastic portion of the demand curve? If the monopolist can price discrimination (3rd-degree price discrimination) then in which market he is likely to charge higher price one with a lower elasticity of demand or with higher elasticity of demand?
Marginal revenue is negative on the lower portion of the demand curve(the inelastic portion of the demand curve). For monopoly equilibrium, Marginal Revenue(MR)= Marginal Cost(MC), as MC is always positive so monopolist will never produce in the inelastic portion of the demand curve. P = MC/([ 1 - 1/E ]) For the value of E< 1 denominator becomes negative that means the price changed is negative for given positive MC. As price changed can never be negative monopolist will not produce on the inelastic portion of the demand curve Equilibrium condition under Multimarket monopolist is MR1= MR2= MC P 1 [ 1 - 1/E1 ] = P2 [ 1 - 1/E2 ] = MC where E1 , E2 are elasticity of demand in market 1 and 2 So now (P 1 )/P2 = ([ 1 - 1/E2 ] )/([ 1 - 1/E1 ] ) ……………………1 Now consider E2 > E1 1/E1 > 1/E2 Multiply both sides by negative -1/E1 < - 1/E Add 1 to both sides 1- 1/E1 <1- 1/E1 using the above inequality in 1, the Denominator is smaller than the numerator so the fraction will be greater than 1. Hence we get (P 1 )/P2>1 so P 1> P2 i.e price discriminating monopolist will charge a higher price in the market where the elasticity of demand is lower in comparison to the market elasticity of demand is greater.
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