Consider a portfolio consisting of two stocks S1 and S2, where S, denotes the value at...

 

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Consider a portfolio consisting of two stocks S1 and S2, where S, denotes the value at time t of stock 1 in EUR and S₁,2 denotes the value at time t of stock 2 in CHF. Let e, be the CHF-EUR exchange rate at time t, that is 1 CHF= e, EUR, at time f. Let A₁ and ₂ be the number of shares of stock 1 and stock 2 in the portfolio respectively. Assume that from t to + 1, the portfolio composition stays the same. (a) Derive the value V, of the portfolio at time in EUR, in terms of the risk factors Zt1 = log St,₁. Z₁,1 = log S₁,1 and 2₁,1 = loge,. What is the corresponding mapping? (b) Derive the value V₁+1 of the portfolio at time t + 1 in EUR in terms of the risk factors Z for j = 1,2,3 and the risk factor changes X+13=Z+Ztj. for j = 1,2,3. (c) Derive the 1-period ahead loss L+1 (d) Derive the 1-period ahead linearized loss L (e) Express the linearized loss in terms of portfolio weights ₁, 2, where w, is the percent- age of total wealth invested in each stock. (f) Consider equal portfolio weights. Suppose that stock 1 increases by 3%, stock 2 increases by 2% and that EUR loses 1% of its value against CHF. Compute the linearized loss (in percentage). Consider a portfolio consisting of two stocks S1 and S2, where S, denotes the value at time t of stock 1 in EUR and S₁,2 denotes the value at time t of stock 2 in CHF. Let e, be the CHF-EUR exchange rate at time t, that is 1 CHF= e, EUR, at time f. Let A₁ and ₂ be the number of shares of stock 1 and stock 2 in the portfolio respectively. Assume that from t to + 1, the portfolio composition stays the same. (a) Derive the value V, of the portfolio at time in EUR, in terms of the risk factors Zt1 = log St,₁. Z₁,1 = log S₁,1 and 2₁,1 = loge,. What is the corresponding mapping? (b) Derive the value V₁+1 of the portfolio at time t + 1 in EUR in terms of the risk factors Z for j = 1,2,3 and the risk factor changes X+13=Z+Ztj. for j = 1,2,3. (c) Derive the 1-period ahead loss L+1 (d) Derive the 1-period ahead linearized loss L (e) Express the linearized loss in terms of portfolio weights ₁, 2, where w, is the percent- age of total wealth invested in each stock. (f) Consider equal portfolio weights. Suppose that stock 1 increases by 3%, stock 2 increases by 2% and that EUR loses 1% of its value against CHF. Compute the linearized loss (in percentage).

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a The value Vt of the portfolio at time t in EUR can be expressed as Vt A1S1t A2S2t where A1 is the ... View the full answer