L24 & L25: PORTFOLIO BALANCE Questions –How can we allow for effects of debt even if it is not monetized ? Effects of budget deficits, current account deficits, & sterilized forex intervention. –How can we allow for effects of risk? Currency risk. Country risk. –How can we bring more information to bear on the structure of investors’ asset demands? Key parameters –Risk-aversion –Variance of returns –Covariances among returns.

Each investor at time t allocates shares of his or her portfolio to a menu of assets, as a function of expected return, risk, & perhaps other factors (tax treatment, liquidity...): Sum across investors i to get the aggregate demand for assets, which must equal supply in the market. We will invert the function to determine what E t r t +1 must be, for supplies x t to be willingly held. x i, t = β i (E t r t+1, risk ).

The general portfolio balance case: Tobin ( 1958, 1969 )  lots of assets (M, Bonds, Equities), with different attributes &  lots of investors with different preferences. But we will focus more on one-period bonds, & assume uniform preferences among relevant investors. Lecture 24 assumption (especially relevant for rich countries): exchange risk is the only important risk. Lecture 25 assumption (esp. relevant for developing countries): default risk is important.

PORTFOLIO DIVERSIFICATION Motivating questions for Portfolio Balance Model: « How should you manage a portfolio, e.g., a Sovereign Wealth Fund ? Starting point: Most investors care not just about expected returns, but also about risk. => rp ≠ 0 => UIP fails. They wish to diversify their portfolios. « How do we think about effects of: * Current account deficits, * Budget deficits, and * (sterilized) forex intervention, which had no effects in monetary models? « What determines the risk premium? How large is it?

OPEN-ECONOMY PORTFOLIO BALANCE MODEL Demand for foreign assets by investor i: x i, t = A i + B i E t (r f t+1 – r d t+1 ) ; where x is the share of the portfolio allocated to foreign assets, vs. domestic. « For this lecture, assume foreign assets all denominated in $ ( and/or €, ¥, etc.), and domestic assets all denominated in dirham (domestic currency); Then portfolio share x i ≡ SF i / W i, « Assume, further, no default risk. Then expected real return differential = exchange risk premium rp t ≡ i $ t – i d t + E t ∆s t+1 where W i ≡ D i + S F i ≡ total wealth held; D i ≡ domestic assets held, F i ≡ foreign assets held, and S = exchange rate. So x i, t = A i + B i rp t.

Financial market equilibrium: assets held = assets supplied…. « where aggregate portfolio share x t ≡ S F t / W t, « W ≡ D + SF ≡ total wealth held, « F ≡ total foreign ($) assets held, & « D ≡ total domestic assets held. Sum asset demands across all investors in the marketplace: Total demand for foreign assets ≡ x t ≡ Σ [ x i, t ] = Σ [ A i + B i rp t ] x t = A + B rp t and for now assume them to have identical parameters A i =A and B i =B :

« In general, x foreigners > x local residents (Home bias). How do asset supplies get into the market? « Domestic debt is issued by the government: In extreme “small-country case,” x foreigners = 1 => only local residents’ holdings are relevant. Then aggregate supply of foreign assets given by:.

Now invert: rp t = B -1 x t - B -1 A. Special case : | B -1 | = 0, perfect substitutability ( |B|=∞ ), no risk premium (rp t = 0), and so no effect from sterilized forex intervention. We see that asset supplies are a determinant of the risk premium. To repeat, x t = A + B rp t.

How the supply of debt x determines the risk premium rp in the portfolio balance model A large x forces up the expected return that portfolio holders must be paid.

Now assume investors diversify optimally “Don’t put all your eggs in one basket.”

“MANAGEMENT OF COMMODITY REVENUES – BOTSWANA’S CASE” by Linah Mohohlo, Governor, Bank of Botswana Allocation of Portfolio between Bonds & Equity in the Pula Fund very safe very risky ½ & ½

Efficient Frontier: Allocation of Portolio between Bonds (“Fixed Income”) & Equity “MANAGEMENT OF COMMODITY REVENUES – BOTSWANA’S CASE” by Linah Mohohlo, Governor, Bank of Botswana very safe very risky ½ & ½

Optimally Diversified Portfolios x t = A + B rp t = Minimum-variance portfolio + Speculative portfolio Under certain assumptions, => same problem as to maximize Φ [E(W +1 ), V(W +1 )], Φ 1 > 0, Φ 2 <0. End-of-period wealth W +1 Problem: Choose x t to maximize E t [ U( W t+1 ) ] [

Optimal diversification Define, RRA ≡, & V  V( r $ +1 – r d +1 ). Then, which matches for the optimal-diversification case B -1 = ρ V and. } First-order condition: = 0.

For example, if goods prices are nonstochastic and s +1 is the only source of uncertainty, then V = Var(  s +1 ) Also, depending how rp is defined, rp may differ from i - i* - E  s by a convexity term = (α – ½) V. (See resolution of Siegal paradox, in latter part of Addendum to forward bias lecture.) and A = α, the share of foreign goods in consumption basket. E.g., if all consumption is domestic (A=α =0), domestic bonds are safe; very risk-averse investors do not venture abroad (because Cov (r d, r $ -r d ) = 0). A is the minimum-variance portfolio ( in x = A + [ρV] -1 rp): It’s what an investor holds if risk-aversion ρ = ∞.

Equities: Whatever is risk-aversion ρ, the optimal portfolio allocates a substantial share abroad, because the min-variance portfolio does. Who holds what portfolio? A foolishly under- diversified American The most risk-averse Moderately risk-averse Very risk-tolerant

And yet in practice, Americans hold most of their portfolio in US securities, Japanese hold theirs in Japanese securities, Etc.

Addendum 1: Beyond the small-country model Foreign residents are in the market for domestic vs. foreign assets, alongside home residents, with weights w H vs. w F. Now aggregate:. A difference in consumption preferences,  H some preference for local assets, A H < A F (home bias). If the domestic country runs a CA surplus => Its share of world wealth, w H, rises over time, and foreigners’ share falls. => Domestic preference, A H, receives increasing weight in total global demand. => Global demand for domestic assets rises. => Required expected return falls.

Further evidence on home bias in US Equity shares are based on 1997 comprehensive survey of U.S. residents’ holdings of foreign securities. Bias column ≡ 1 minus (foreign equity share / world market share). If U.S. investors held foreign securities in proportions equal to those in the world equity market benchmark, bias would = 0. From : G.Baekert & R.Hodrick, Intl. Fin.Management, Feb. 2004, Table 14.16, Panel A Source: Based on Table 1, in Ahearne, Griever & Warnock (2002). Country Share in U.S. Bias Equity Portfolio Spain Australia Hong Kong Mexico Brazil India China Taiwan Russia South Africa Country Share in U.S. Bias Equity Portfolio US UK Japan France Canada Germany Italy Netherlands Switzerland Sweden

But international diversification is rising steadily Proportion of foreign bonds + equities in total equity + bond portfolios of residents in the reported countries. From a 2002 UBS Asset Management study. Source: G. Baekert & R. Hodrick, op.cit., Table 14.16, Panel B US 4% 11% Japan 12% 27% The Netherlands 12% 62% UK 23% 26% Switzerland 11% 21% Australia 14% 19% Sweden 4% 25%