格拉斯哥大学 (University of Glasgow)：汇率讲座之购买力平价及利率平价

Purchasing Power Parity (PPP)
购买力平价（PPP）

• Purchasing power parity (equal spending power) would count for two countries if LOOP held for all goods and services:
购买力平价（平等消费权）指望两个国家如果循环举行的所有商品和服务：
• 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 - 简要
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)
利率平价（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.’
利率平价又来自一价法（LOOP）：等于风险资产应该提供相同的回报，无论面额的货币。
    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
有两个原因参加外汇 - 出口/进口商品和服务，或用于海外投资
• Purchasing power parity suggests that the exchange rate will change until goods’ & services’ prices are equivalent.
购买力平价，表明汇价将改变，直到货物及服务的价格是相等的。
• Interest rate parity suggests instead that it adjusts until returns on domestic and overseas investments are equivalent.
利率平价理论，而不是建议调整，直到国内和海外投资的回报是相等的。
• There exist two types of interest parity – covered and uncovered interest parity.
存在两种类型的利率平价 - 覆盖与抛补利率平价。

Uncovered Interest Parity
无抛补利率平价

• Uncovered Interest Parity (UIP)
• rUK = rUS + [(£/$S - £/$Se)/ £/$S]
Where:
$/£S = the ‘spot’ market rate of $s to buy £s today#p#分页标题#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
汇率报价

• 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??
汇率事宜？

1. When you move money from the UK to the US, the UK exchange rate matters – the number of $s per £1
当您将钱从英国到美国，英国汇率事宜 - $ s的每1英镑
e.g. £100 becomes 100 x S$/£
this would be  100 x 2 ($s per £)= $200
例如£100成为100个S/美元英镑,
这将是100×2（$ s每英镑）=200美元
2. You then invest this in a US government security paying 5% for a year:
然后，您可以投资在美国政府的安全支付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)
然后你的钱转移回了家 - 所以你必须使用美国的货币市场 - 他们率为0.5（£s每1美元，）
$210 x 0.5 = 105 (now £s)
• This would be equivalent to investing in the UK at 5%, which would also have paid £105.
这将相当于在英国投资的5％，这也将支付105英镑。
• But this assumes the £/$ exchange rate (in US) didn’t get any worse!
但是这个假设，英镑/美元的汇率在（美国）没有得到任何更糟！

Expected returns
预期回报

• If a UK investor puts £1 into a government bond for a year, it will be worth £1.(1+rUK).
如果一个英国投资者将1到一年的政府债券，这将是英镑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
如果他们选择到美国政府债券，他们将不得不做两个外汇交易 - 改变自己的1英镑成美元的合同开始，改变美元在年底为英镑£s后支付
• The expected value of this investment would equal:#p#分页标题#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…
但是这种投资受到外汇风险

Covered Interest Parity
补利率平价

• Covered Interest Parity (CIP) involves the use of forward contracts to remove risk of foreign exchange changes
补利率平价（CIP）涉及使用远期合约，以消除外汇变动风险
• If a UK investor puts £1 into a government bond for a year, it will be worth £1.(1+rUK).
如果一个英国投资者将1到一年的政府债券，这将是英镑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
如果他们选择到美国政府债券，他们会做两外汇交易 - 但在这里，他们改变他们的1英镑成美元的合同开始，并同时进入一个改变美元的远期外汇合约在年底的投资为英镑£s后支付