I mean, hypothetically a bond trading at $.60 on the dollar with an 8% coupon, five-year bond that's yielding about 18%.
我的意思是,假设一种债券以0。60美元进行交易,同时有8%的票息,五年期债券收益率在18%左右。
So, if it's a four-year bond, it would trade at about $90, 6% so it would be yielding 6%.
所以,如果这是四年期的债券,那么它可能在大约90美元左右进行交易,因此它的收益率大约在。
At least in the domestic equity world you've got a pretty stable base that you were looking at ten years ago.
至少对于国内股市来说,当你回顾10年前的收益率,会得到一个非常稳定的基准数字
One more thing, I said they're not independent, so we have to talk about the covariance between the returns.
还有,我说过它们不是相互独立的,因此我们还需要讨论两个收益率的协方差。
If you're comparing two portfolios with the same expected return, then you want the one with the lower variance.
比较两个有相同预期收益率的投资组合时,你会选择方差小的那一个。
Moreover, it's had a 17.8% average return for the last ten years, which is number one among university endowments.
甚至,过去十年中,耶鲁基金的年均收益率高达17.8%,依然高居全美高校榜首
It shows the standard deviation of the return on the portfolio as a function of the expected return on the portfolio.
它是投资组合的收益标准差,关于预期收益率的函数图像。
They like to--when they're computing the investment yield, they want to be completely honest and not use any rules of thumb.
当他们计算投资收益率的时候,他们需要完全精确,而非用经验公式
Then finally, the final step is to find what is the tangency line that goes through the riskless rate.
在最后,最终的步骤是找出一条,穿过无风险收益率的切线。
So Yale had a 28% return on its portfolio last year, which was number one of all college endowments.
去年耶鲁基金获得了28%的收益,收益率高居全美高校榜首
The difference between the average return for colleges and universities and Yale's returns has added $14.4 billion dollars to the University's coffers.
其他高校的平均收益率,与耶鲁的收益率的差距,为耶鲁财政增加了144亿美元
.. The equity premium is the-- 2.8% this short-term 2.8% is the riskless return, historically, for a period of almost 200 years.
股权溢价就是-,这个短期无风险投资收益率是,是根据近200年的数据得出的。
In fact, different people might make different choices about how much risk they're willing to bear to get a higher expected return.
事实上,为了获得高的预期收益率,人们愿意承受的风险,也会不同。
The yield-to-maturity on an indexed bond is already in real terms because the coupons are indexed to inflation.
这种债券的到期收益率,就是实际收益率,因为票息已经被通胀指数化了
So, I've got here a term structure; well, the term structure is the plot of yield-to-maturity against time-to-maturity.
我这有一张期限结构图,期限结构其实是,到期收益率与到期期限之间的关系图
If you looked at the domestic equity return -the average return that was posted in 2000--it was -3.1%.
看看国内证券的收益,2000年公报的平均收益率是负3.1%
Now I don't know how impressed you are, the year before that it was 22% in one year.
我不知道给你们是否被震撼到了,前年的收益率是22%
I computed the average return on stocks over that time period and I computed the average return on bonds over that time period.
我计算了那个时间段的股票平均收益率,和债券平均收益率。
So,the combination of survivorship bias and backfill bias for that one year made 4.3 percentage points difference.
因此在生存偏差和回填偏差的共同作用下,造成了两个收益率之间4.3%的差值
Let's suppose that all of them are the same-- they all have the same standard deviation.
我们假设这些资产的收益率标准差-,均相等。
The fact that people look at quarterly returns of mutual funds is incredibly dysfunctional.
只关注基金的季度收益率,是相当不妥当的的
So, that is not--your return is actually higher than 2.51% on an annualized basis.
所以,你的实际年收益率,应该高于2.51%
The return he got from 1996 to 2006 was 17% a year on investments.
从1996到2006,他的个人投资收益率为一年17%
To calculate the expected utility of your wealth, you might also have to look at the expected return, or the geometric expected return, or the standard deviation.
要计算你财富的期望效用,你也许还要研究预期收益曲线,或几何预期收益率,或是标准差
2% You could say, I think my portfolio has an expected return of 12%-- that would be better than if it had an expected return of 10%.
如果一个投资组合的预期收益率有-,那就比一个只有10%的投资组合要好。
We often assume in finance that random variables, such as returns,are normally distributed.
金融学中我们常假设随机变量,例如收益率,是服从正态分布的
So, that's how you go from the discount rate to the investment rate.
这就是从折扣率到投资收益率的换算过程
Last year the return on the Yale portfolio was 28% in one year.
去年耶鲁大学投资组合的收益率,是28%
This is the return on stocks for a period of almost 200 years.
这个是200年内股票的投资收益率。
Remember, this thing only runs for sixty days and you could compute your sixty-day return, but people like to compare annual returns-- once again, a tradition we have.
注意,这个债券期限只有60天,当然你可以计算60天的收益率,但是人们往往喜欢用年收益率进行比较,这也是一种传统
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