格拉斯哥大學 (University of Glasgow)：匯率講座之購買力平價及利率平價

Purchasing Power Parity (PPP)
購買力平價（PPP）

• Purchasing power parity (equal spending power) would count for two countries if LOOP held for all goods and services:
購買力平價（平等消費權）指望兩個國家如果循環舉行的所有商品和服務：
• LOOP:  Pi$ = $/£ELOOP. Pi£
• PPP:
aUSSPi$ = E$/£. aUK SPi£
Where:
aUS,UK = ‘weights’ on US/UK spending on items
E = exchange rate (loop for single items, or overall exchange rate)
S = summation sign for all i = 1 to ‘n’
P$/£ = prices of US/UK items

PPP – in brief
PPP - 簡要
http://ukthesis.org/gjswglzy

• As ‘aUSSPi$’  is really just a price index for the USA, this can be rewritten:
   PUS=S$/£.PUK
or  P*=S.P
Where:
PUS/UK= a price index for the US/UK; or
P* = ‘foreign’ price level;
S($/£)= is the ‘spot’ market exchange rate.
N.B. – if you ever get strange results from this, check the way the exchange rate has been calculated!

Interest Rate Parity (IRP)
利率平價（IRP）

“
• Interest rate parity again comes from the Law of One Price (LOOP):  ‘assets of equal risk should offer the same return, regardless of the currency of denomination.’
利率平價又來自一價法（LOOP）：等于風險資產應該提供相同的回報，無論面額的貨幣。
    Eaker et al. p.126
• There are two reasons for participating in foreign exchange – exporting/importing goods and services, or for purposes of overseas investment
有兩個原因參加外匯 - 出口/進口商品和服務，或用于海外投資
• Purchasing power parity suggests that the exchange rate will change until goods’ & services’ prices are equivalent.
購買力平價，表明匯價將改變，直到貨物及服務的價格是相等的。
• Interest rate parity suggests instead that it adjusts until returns on domestic and overseas investments are equivalent.
利率平價理論，而不是建議調整，直到國內和海外投資的回報是相等的。
• There exist two types of interest parity – covered and uncovered interest parity.
存在兩種類型的利率平價 - 覆蓋與拋補利率平價。

Uncovered Interest Parity
無拋補利率平價

• Uncovered Interest Parity (UIP)
• rUK = rUS + [(£/$S - £/$Se)/ £/$S]
Where:
$/£S = the ‘spot’ market rate of $s to buy £s today#p#分頁標題#e#
$/£Se = the expected ‘spot’ market rate at the end of the investment
$/£S - $/£Se = the extra income from any appreciation of the exchange rate over the value expected for the end of the investment
r = interest rate in the UK (£) or US ($)
Source:  Econ 405B Lecture Two pp.9-11

Exchange rate quotes
匯率報價

• UK quote exchange rates as number of $s for £1 – S$/£
• US quote them as number of £s for $1 (reverse) – S£/$
• Technically, one is the inverse of the other so that:
  S$/£ = 1 / S£/$
E.g. If UK exchange rate is $2 (per pound) US exchange rate is…. ½ = 0.5 (£s per $)

Which exchange rate matters??
匯率事宜？

1. When you move money from the UK to the US, the UK exchange rate matters – the number of $s per £1
當您將錢從英國到美國，英國匯率事宜 - $ s的每1英鎊
e.g. £100 becomes 100 x S$/£
this would be  100 x 2 ($s per £)= $200
例如£100成為100個S/美元英鎊,
這將是100×2（$ s每英鎊）=200美元
2. You then invest this in a US government security paying 5% for a year:
然后，您可以投資在美國政府的安全支付5％的一年：
Value then = $200 x (1+0.05)
       = $210
3. You then transfer the money back home – so you have to use the US money markets – where their rate was 0.5 (£s per $1)
然后你的錢轉移回了家 - 所以你必須使用美國的貨幣市場 - 他們率為0.5（£s每1美元，）
$210 x 0.5 = 105 (now £s)
• This would be equivalent to investing in the UK at 5%, which would also have paid £105.
這將相當于在英國投資的5％，這也將支付105英鎊。
• But this assumes the £/$ exchange rate (in US) didn’t get any worse!
但是這個假設，英鎊/美元的匯率在（美國）沒有得到任何更糟！

Expected returns
預期回報

• If a UK investor puts £1 into a government bond for a year, it will be worth £1.(1+rUK).
如果一個英國投資者將1到一年的政府債券，這將是英鎊1（1 + RUK）。
• If they chose to put this into a US government bond, they would have to do two foreign exchange deals – change their £1 into dollars at the start of the contract, and change the dollars paid back into £s at the end
如果他們選擇到美國政府債券，他們將不得不做兩個外匯交易 - 改變自己的1英鎊成美元的合同開始，改變美元在年底為英鎊£s后支付
• The expected value of this investment would equal:#p#分頁標題#e#
  £1.$/£S.(1+rUS).£/$Se
Where:
 £/$Se = expected spot exchange rate of £s for $s in the US foreign exchange market – could be written as (1/$/£Se) i.e. the inverse of the expected spot rate $s per £ in the UK market
• But this investment is subject to foreign exchange risk…
但是這種投資受到外匯風險

Covered Interest Parity
補利率平價

• Covered Interest Parity (CIP) involves the use of forward contracts to remove risk of foreign exchange changes
補利率平價（CIP）涉及使用遠期合約，以消除外匯變動風險
• If a UK investor puts £1 into a government bond for a year, it will be worth £1.(1+rUK).
如果一個英國投資者將1到一年的政府債券，這將是英鎊1（1 + RUK）。
• If they chose to put this into a US government bond, they would have to do two foreign exchange deals – but here they change their £1 into dollars at the start of the contract, and simultaneously enter a forward exchange contract to change the dollars paid back into at the end of the investment
如果他們選擇到美國政府債券，他們會做兩外匯交易 - 但在這里，他們改變他們的1英鎊成美元的合同開始，并同時進入一個改變美元的遠期外匯合約在年底的投資為英鎊£s后支付