ICAPM 和 CAPM 的關係是什麼？

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如果你說的ICAPM是Merton的Intertemporal CAPM的話，其實很好理解。

先簡要回溯一下CAPM的特點。（這段可以略過直接從CAPM的公式看起）

1. 單期模型
2. 投資者的目標是最大化效用(Utility)
3. 投資者的效用只跟兩個參數有關，投資組合的預期收益和投資組合的波動率
4. 投資者是理性的，厭惡風險的
5. 所有投資者的風險偏好都是一樣的，他們有唯一的風險厭惡參數
6. 市場是無摩擦的市場（No friction),這意味著沒有交易費用
7. 投資者沒有能力影響市場價格
8. 投資者有能力以無風險利率借到任意數目的錢
9. 所有的投資者有同樣的信息和對市場的期望

最後得到一個簡單的公式

即資產的超額收益，或者說風險溢價（risk premium)，跟市場的風險溢價成一個線性正比關係，其中Beta被用來衡量線性關係的敏感度。

如果你願意你可以針對上面的任何一條假設進行修改，你就可以得到一個新的模型。Merton 1973 http://www.people.hbs.edu/rmerton/Intertemporal%20Capital%20Asset%20Pricing%20Model.pdf 主要是把原有的一期模型改變成了多期模型。也沒什麼特別的，記得我們的模型參數有3個

,

現在假設他們是隨時間變化的。也就說，資產的預期收益率是隨時間變化的，可以是滿足一個隨機過程，或者是變成了一個時間的函數，所以我們的參數就變成了帶上時間的下標

它們的取值範圍就界定了我們可以做出來的投資決策。你把他們想像成下廚的材料，不同食材的數目不一樣你可以做的菜不一樣。所以它們的取值範圍我們稱作投資組合機會集（Investment Opportunity Set)。

當你只有一期投資決策的時候，這個不是什麼問題，但是當你有多期投資決策的時候，你就要考慮到 —— 當下這期決策的結果會影響到你下一期的投資機會。就好像你做菜鹽用完了就後面什麼也做不了，所以你得悠著點。既然如此，你就知道了，你在做投資決策的時候得擔心，假如這個資產的收益率劇烈變動我怎麼辦？如果一個資產的收益率是預期隨時間遞減的，那我應該相應地減少它在我的投資組合中所佔的比重不是嗎？所以你需要對沖參數隨時間變化的風險。所以你要把未來很多期的參數都考慮進來。最後你會得到一個很類似CAPM的公式，如下

多出來的後面幾項就是帶的就是我說的對沖項（hedge），這就是ICAPM了。我喜歡寫成減號，比較能夠體現對沖的意義，不過你也知道代數上沒什麼區別，你也可以寫成加號。至於具體這裡的的具體形式就不寫了，對於理解模型的本質沒有太大幫助。事實上我可以通過不同的假設推出完全不同的來。

這個時候你仔細一看，這不就是多因子模型嗎？不完全是，Factor Model是通過另外一個套路推出來的，不過大家殊途同歸。APT（套利定價理論）、多因子模型、Fama-French模型這三者的關係是怎樣的？ - 陳皇宇 Renco 的回答

我覺得我已經廢話太多了，如果哪個地方沒講清楚留言我再更正吧。

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ICAPM是International capital asset pricing model, CAPM是capital asset pricing model，兩者區別在於：

第一：ICAPM相關的市場風險是全球風險，不是國內市場風險

第二：ICAPM額外的風險溢價是和資產對貨幣變動的敏感程度相關聯的。

下面有一些資料，題主不清楚的話可以看看。

Investing in any asset has risks that can be minimized by using financial tools to determine expected returns. The capital asset pricing model (CAPM) is one of these tools. This model calculates the required rate of return for an asset using the expected returnon both the market and a risk-free asset, and the asset"s correlation or sensitivity to the market.

Some of the problems inherent in the model are its assumptions, which include: no transaction costs; no taxes; investors can borrow and lend at the risk-free rate; and investors are rational and risk averse. Obviously these assumptions are not fully applicable to real-world investing. Despite this, CAPM is useful as one of several tools in estimating the return expected on an investment.

The unrealistic assumptions of CAPM have led to the creation of several expanded models that include additional factors and the relaxing of several assumptions used in CAPM. International CAPM (ICAPM) uses the same inputs as the CAPM but also takes into account other variables that influence the return on assets on a global basis. As a result, ICAPM is far more useful than CAPM in practice. However, despite relaxing some assumptions, ICAPM does have limitations that impact its practicality.

Understanding ICAPM Calculations

Since ICAPM introduces additional variables or factors to the CAPM model, investors first need to understand CAPM"s calculations. CAPM simply states investors want to be compensated for:

1. The time value of money, which they expect to be more than the risk-free rate and;
2. Taking market risk so they require a premium over the return of the market, less the risk-free rate, times the correlation with the market.

ICAPM expands on CAPM, further saying that in addition to getting compensated for the time value of money and the premium for taking market risk, investors need to be paid for direct and indirect exposure to foreign currency. ICAPM allows investors to add currency effects to CAPM to account for the sensitivity to changes in foreign currency when investors hold an asset. This sensitivity accounts for changes in a currency that directly and indirectly affects profitability and, thus, returns.

For example, if a company domiciled in the United States buys parts from China and the U.S. dollar strengthens relative the Chinese Yuan, then the costs of those imports goes down. This indirect currency exposure impacts the profitability of a company and the returns generated by the investment. To determine these effects, investors need to calculate the difference between the expected future spot exchange rate and the forward rate, and divide that difference by today"s spot rate, the result of which is the foreign currency risk premium (FCRP). Then, multiply that by the sensitivity of the domestic currency returns to changes in foreign currencies. ICAPM provides investors with a way of calculating expected returns in local currency terms by accounting for variables as stated below:

Expected Return= RFR+B(Rm-Rf)+(Bi*FCRPi)where:

RFR = domestic risk free rate

Rm-Rf = premium for global market risk measured in investor"s local currency

Bi*FCRPi= foreign currency risk premium

Assumptions

While ICAPM improves upon the unrealistic assumptions of CAPM, several assumptions are still required for the theoretical model to be valid. The most important assumption is that international capital markets are integrated. If this assumption fails and international markets are segmented, then there will be pricing discrepancies among assets with similarrisk profiles but in different currencies. As a result, segmented markets will cause investors to make higher allocations to specific assets in specific countries, resulting in inefficient asset pricing. ICAPM also assumes unlimited lending and borrowing at the risk-free rate.

Practical Uses

ICAPM"s usefulness in stock selection and portfolio management is only as good as understanding the assumptions as stated above. Despite these limitations, portfolio selection can be influenced by the model. Understanding the impact of currency movements on a particular company"s operations and profits will help investors choose among two assets with similar characteristics in different countries.

For example if an investor in the U.S. wants to calculate the expected return from holding asset A and compare that to the expected return from holding asset B, he needs to determine the inputs for the last two components of the model, which are to determine the direct currency impact and the indirect currency impact. The first two variables in the equation will be the same for both assets. Therefore, the practical usefulness of the ICAPM is in understanding how one currency affects a company in the foreign country and how translating it to the investor"s local currency will impact the return on the asset.

For example: An investor is deciding to invest in one of the following assets:

• Company A: Japanese company that derives all of its profits and input costs in Yen
• Company B: Japanese company that derives all its profits in U.S. dollars but has input costs in Yen

Both assets have similar betas, or sensitivity to changes in world market portfolio. In a macroeconomic environment where the U.S. dollar is weakening relative to the Japanese Yen, an investor will determine that the profits for Company B would decline, as it would cost more U.S. dollars to buy the products. As such, the required return would increase for Company B, relative to Company A, to offset the additional currency risk.

The Bottom Line

ICAPM is one of several models used to determine the required return on an asset. Used in conjunction with other financial tools, it can assist investors in selecting assets that will meet their required rate of return. ICAPM, like CAPM, makes several assumptions, including that global markets are integrated and efficient. If this assumption fails, then stock selection is critical; allocating more resources toward investments in countries that have a currency advantage should result in alpha. Currency advantages tend to disappear quickly as exploited market inefficiencies close, but the fact that these inefficiencies occur argues that active portfolio management is key to providing superior returns over the market portfolio.

Read more: Introduction To International CAPM | InvestopediaIntroduction To International CAPM

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